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Klaas G., Leedham-Green C.R., Plesken W. — Linear Pro-p-Groups of Finite Width
Klaas  G., Leedham-Green C.R., Plesken W. — Linear Pro-p-Groups  of Finite Width

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Название: Linear Pro-p-Groups of Finite Width

Авторы: Klaas G., Leedham-Green C.R., Plesken W.


The normal subgroup structure of maximal pro-"p"-subgroups of rational points of algebraic groups over the "p"-adics and their characteristic "p" analogues are investigated. These groups have finite width, i.e. the indices of the sucessive terms of the lower central series are bounded since they become periodic. The richness of the lattice of normal subgroups is studied by the notion of obliquity. All just infinite maximal groups with Lie algebras up to dimension 14 and most Chevalley groups and classical groups in characteristic 0 and "p" are covered. The methods use computers in small cases and are purely theoretical for the infinite series using root systems or orders with involutions.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 115

Добавлена в каталог: 04.12.2009

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Предметный указатель
"A and B"      I.3.4
$(g_{i})_{i\in I}$ (extension to products of the family $(g_{i})_{i\in I}$, by abuse of language)      II.5.7
$(t_{i})_{P\{i\}}$, $(t_{i})_{a\leqslant i\leqslant b}$      III.5.4
$(x_{i})_{i\in I}$, $(x_{i})$      R.2.14
$(x_{n})$, $(x_{m,n})$ (m,n natural integers)      R.7.8
$(x_{n})_{P\{n\}}$, $(x_{n})_{k\leqslant n}$, $(x_{n})_{n\geqslant k}$, $(x_{n})$      III.6.1
$(\exists x)R$, $(\forall x)R$      I.4.1
$(\exists_{A}x)R$, $(\forall_{A}x)R$      I.4.4
$(\frac{\mathfrak{n}}{\mathfrak{p}})$ (n,p integers)      III.5.8
$<f_{1},...,f_{n}>^{S}$ (S an echelon construction scheme, $f_{1}$,...,$f_{n}$ mappings)      IV.1.1
$A\cup B$, $A\cup B\cup C$, $A\cap B$, $A\cap B\cap C$      II.4.5
$A\times B$, $A\times B\times C$, $A\times B\times C\times D$, (x,y,z)      II.2.2
$B\circ A$, BA, $G\circ B\circ A$, CBA (A a subset of $E\times F$, B a subset of $F\times G$, C a subset of $G\times H$)      R.3.10
$Coll_{X}R$, $\mathscr{E}_{X}(R)$      II.1.4
$E\times F$ (E,F sets)      R.3.1
$E\times F\times G$      R.3.12
$E^{I}$ (E,I sets)      R.4.9
$f^{n}$ (f a mapping}      III.6.2
$f_{A}$ (f a mapping)      R.2.13
$g\circ f$, $h\circ g\circ f$ (f,g,h mappings)      R.2.11
$G\limits^{-1}$ (G a graph), $\Gamma\limits^{-1}$ ($\Gamma$ a correspondence)      II.3.2
$G^{'}\circ G$, $G^{'}G$ (G, $G^{'}$ graphs), $\Gamma^{'}\circ \Gamma$, $\Gamma^{'}\Gamma$ ($\Gamma$, $\Gamma^{'}$ correspondences)      II.3.3
$Is(\Gamma,\Gamma^{'})$, Ord(E), $\lambda\prec\mu$, $\sum\limits_{i\in I}\lambda_{i}$, $P\limits_{i\in I}\lambda_{i}$, $\lambda +\mu$, $\mu\lambda$, $\lambda^{*}$ ($\lambda,\mu,\lambda_{i}$ orde types)      III.2 Exercise
$pr_{1,2}$      R.3.12
$pr_{1}$, $pr_{2}$      II.3.6 R.3.1
$pr_{1}<G>$, $pr_{2}<G>$, $pr_{1} G$, $pr_{2} G$ (G a graph)      II.3.1
$pr_{J}$      II.5.4
$pr_{J}$, $pr_{\alpha}$      R.4.11
$R\times R^{'}$ (R, $R^{'}$ equivalence relations)      II.6.8
$R\times S$ (R,S equivalence relations)      R.5.10
$R_{A}$ (R an equivalence relation, A a set)      II.6.6
$R_{A}$ (R an equivalence relation, A a subset)      R.5.5
$S(E_{1}...,E_{n})$ (S an echelon construction scheme, $E_{1}$,...,$E_{n}$ sets)      IV.1.1
$sup_{E}X$, $inf_{E}X$      III.1.9
$sup_{E}X$, sup X, $inf_{E}X$, inf X      R.6.7
$S_{x}$      III.2.1
$u\times v$ (u, v functions), (u, v) (by abuse of language)      II.3.9
$x\equiv y$ (mod R) (R an equivalence relation)      II.6.1
$x\leqslant y$, $y\geqslant x$, $x\nleqslant y$      III.1.3
$x\rightarrow T (x\in A, T\in C)$, $x\rightarrow T (x\in A)$, $x\rightarrow T$, $(T)_{x\in A}$, T (by abuse language) (T a term)      II.3.6
$X_{A}$ (X a subset)      R.1.16
$[\leftarrow,a]$, $]\leftarrow,a[$, $]a,\rightarrow[$, $[a,\rightarrow[$      III.1.13
$\bigcap\limits_{i\in I}X_{i}$, $\bigcap\limits_{i}X_{i}$, $\bigcap\limits_{X\in \mathfrak{F}}X$      R.4.9
$\bigcup\limits_{i\in I}X_{i}$, $\bigcap\limits_{i\in I}X_{i}$      II.4.1
$\bigcup\limits_{i\in I}X_{i}$, $\bigcup\limits_{i}X_{i}$, $\bigcup\limits_{X\in \mathfrak{F}}X$      R.4.4
$\bigcup\limits_{X\in \mathfrak{F}}X$, $\bigcap\limits_{X\in \mathfrak{F}}X$      II.4.1
$\Box$, $\tau$, $\vee$, $\rceil$, $\Longrightarrow$      I.1.1
$\complement A$, E — A      R.1.7
$\complement_{X}A$, X — A, $\complement A$, $\varnothing$      II.1.7
$\cup$, $\cap$      R.1.13
$\Delta$      R.3.4
$\Delta_{A}$, $I_{A}$ (A a set)      II.3.3
$\frac{a}{b}$, a/b (a, b integers such that b divides a)      III.5.6
$\Game$, (T,U), $pr_{1}z$, $pr_{2}z$      II.2.1
$\Gamma<X>$, $\Gamma(X)$, $\Gamma(x)$ ($\Gamma$ a correspondence, X a set, x an object)      II.3.1
$\in$, $\notin$      R.1.7
$\in$, $\notin$, $T\in U$, $T\notin U$      II.1.1
$\leqslant$, $\geqslant$, <, >      R.6.3
$\lim\limits_{\longleftarrow}(E_{\alpha},f_{\beta\alpha})$, $\lim\limits_{\longleftarrow}E_{\alpha}$, $\lim\limits_{\longleftarrow}u_{\alpha}$      R.6.14
$\lim\limits_{\longleftarrow}E_{\alpha}$ ($E_{\alpha}$ sets)      III.7.1
$\lim\limits_{\longleftarrow}u_{\alpha}$ ($u_{\alpha}$ mappings)      III.7.2
$\lim\limits_{\longrightarrow}(E_{\alpha},f_{\beta\alpha})$, $\lim\limits_{\longrightarrow}E_{\alpha}$, $\lim\limits_{\longrightarrow}u_{\alpha}$      R.6.13
$\lim\limits_{\longrightarrow}E_{\alpha}$ ($E_{\alpha}$ sets)      III.7.5
$\lim\limits_{\longrightarrow}u_{\alpha}$ ($u_{\alpha}$ mappings)      III.7.6
$\lim\limits_{\xleftarrow[\alpha,\lambda]{}}E^{\lambda}_{\alpha}$, $\lim\limits_{\xleftarrow[\alpha]{}}E^{\lambda}_{\alpha}$, $\lim\limits_{\xleftarrow[\alpha,\lambda]{}}u^{\lambda}_{\alpha}$, $\lim\limits_{\xleftarrow[\alpha]{}}u^{\lambda}_{\alpha}$      III.7.3
$\lim\limits_{\xrightarrow[\alpha,\lambda]{}}E^{\lambda}_{\alpha}$, $\lim\limits_{\xrightarrow[\alpha]{}}E^{\lambda}_{\alpha}$, $\lim\limits_{\xrightarrow[\alpha,\lambda]{}}u^{\lambda}_{\alpha}$, $\lim\limits_{\xrightarrow[\alpha]{}}u^{\lambda}_{\alpha}$      III.7.7
$\Longleftrightarrow$, $A\Longleftrightarrow B$      I.3.5
$\mathfrak{a}+\mathfrak{b}$, $\mathfrak{a}\mathfrak{b}$ ($\mathfrak{a},\mathfrak{b}$ cardinals)      III.3.3
$\mathfrak{a}^{\mathfrak{b}}$ ($\mathfrak{a},\mathfrak{b}$ cardinals)      III.3.5
$\mathfrak{B}(E)$      R.1.10
$\mathfrak{B}(X)$      II.5.1
$\mathfrak{x}\leqslant\mathfrak{h}$ ($\mathfrak{x}$, $\mathfrak{h}$ cardinals)      III.3.2
$\mathscr{E}_{A}$ ($\mathscr{E}$ a set of subsets)      R.1.16
$\mathscr{F}(E,F)$, $F^{E}$      II.5.2
$\omega_{\alpha}$, $\aleph_{\alpha}$ ($\alpha$ an ordinal)      III.6 Exercise
$\overset{-1}{f}$ (f a mapping)      R.2.6
$\overset{-1}{Z}$ (Z a subset of a product)      R.3.4
$\prod\limits_{i\in I}X_{i}$, $pr_{i}$      II.5.3
$\prod\limits_{i\in I}X_{i}$, $\prod\limits_{i}X_{i}$      R.4.9
$\prod\limits_{P\{i\}}X_{i}$, $\prod\limits^{b}_{i=a}X_{i}$      III.5.4
$\prod\limits_{P\{n\}}X_{n}$, $\prod\limits^{\infty}_{n=k}X_{n}$      III.6.1
$\Sigma$-admissible      IV.3.2
$\sigma$-morphism      IV.2.1
$\subset$, $\supset$, $\not\subset$, $\not\supset$      R.1.12
$\subset$, $\supset$, $\not\subset$, $\not\supset$, $x\subset y$, $x\supset y$      II.1.2
$\sum\limits_{i\in I}a_{i}$, $\underset{i\in I}{P} a_{i}$, $\prod\limits_{i\in I}a_{i}$ ($(a_{i})_{i\in I}$ a family of cardinals)      III.3.3
$\sum\limits_{i\in I}E_{i}$ (ordinal sum)      III.1 Exercise
$\tau_{x}(A)$, (B|x)A, A{x}, A{x,y}, A{B}, A{B,C}      I.1.1
$\underset{i\in I}{sup} a_{i}$ ($(a_{i})_{i\in I}$ a family of cardinals)      III.3.2
$\underset{x\in A}{sup}f(x)$, $\underset{x\in A}{inf}f(x)$      III.1.9 R.6.7
$\underset{x\in A}{sup}x$, $\underset{x\in A}{inf}x$      III.1.9
$\varnothing$      R.1.8
$\varphi_{A}$ (A a subset of a set E)      III.5.5
$\xi^{\eta}$ ($\xi$, $\eta$ ordinals)      III.2 Exercise
($f_{i}$) ($f_{i}$ mappings)      R.4.13
(f,g,h) (f,g,h mappings)      R.3.12
(x,y)      R.3.1
(x,y,z)      R.3.12
0, 1, 2      III.3.1
3, 4      III.4.1
5, 6, 7, 8, 9      III.5.7
=, $\neq$      R.1.6
=, $\neq$, T=U, $T\neq U$      I.5.1
a — b (a,b integers, b<a)      III.5.2
Adjunction (of one set to another)      R.5.4
Adjunction of a greatest element to an ordered set      III.1.7
Agreeing on a set (functions)      II.3.5
Agreement (of two functions on a set)      R.2.14
Aleph      III.6.Ex.10
Antecedent assemblies      I.App.4
Antidirected (ordered set)      III.1.Ex.23
Applying the results of one theory in another      I.2.4
Argument      R.1.2
assembly      I.1.1
Assembly of the first (second) species      I.1.3
Assembly, antecedent      I.App.4
Assembly, balanced      I.App.4
Assembly, perfectly balanced      I.App.4
Associated equivalence relation      II.6.2
Associativity criterion for product structures      IV.2.4
Associativity criterion of the intersection of a family of sets      R.4.8
Associativity criterion of the product of a family of sets      R.4.11
Associativity criterion of the union and intersection of two sets      R.1.14
Associativity criterion of the union of a family of sets      R.4.3
Automorphism      IV.1.5 R.8.6
Auxiliary base sets      IV.1.3 IV.1.4
Auxiliary constant, method of      I.3.3
Auxiliary hypothesis, method of      I.3.3
Axiom of Choice      R.4.10
Axiom of extent      II.1.3
Axiom of infinity      III.6.1
Axiom of the ordered pair      II.2.1
Axiom of the set of subsets      II.5.1
Axiom of the set of two elements      II.1.5
Axiom(s) of a species of structures      IV.1.4
Axiom, explicit      I.2.1
Axiom, implicit      I.2.1
Axioms of structures of the same species      R.8.2
Axioms, equivalent      R.8.4
Balanced assembly      I.App.4
Balanced word      I.App.2
Base of a scale of sets      R.8.1
Base of an expansion, or of a system of numeration      III.5.7
Base sets (of an echelon construction}      IV.1.1
Base sets, auxiliary      IV.1.3 1.4
Base sets, principal      IV.1.3 1.4
Bijection      II.3.7 R.2.9
Bijective mapping      II.3.7 R.2.9
Binomial coefficient      III.5.8
Boolean lattice      III.1.Ex.17
Bound, greatest lower and least upper (of a setora mapping)      III.1.9 R.6
Bound, least upper (of a set of cardinals}      III.3.2
Bound, lower      III.1.8 R.6.7
Bound, strict upper      III.2.4
Bound, upper      III.1.8 R.6.7
Bounded, bounded above, bounded below (set or mapping)      III.1.8 R.6
Branched (ordered set)      III.1..Ex.24
Canonical decomposition of a function      II.6.5 R.5.3
Canonical extension, of a correspondence to sets of subsets      II.5.1
Canonical extension, of a family of functions to the product sets      II.5.7
Canonical extension, of mappings      IV.1.2
Canonical extension, of two functions to the product sets      II.3.9
Canonical extension, signed      IV.2..Ex.1
Canonical injection      II.3.7
Canonical mapping      IV.App.4
Canonical mapping into a direct limit of a direct limit obtained by restriction of the index set      III.7.6
Canonical mapping of $(E\times E')/(R\times R')$ onto $(E/R)\times(E'/R')$      II.6.8 R.5.10
Canonical mapping of $A/R_{A}$ onto f<A>      II.6.6 R.5.5
Canonical mapping of $A^{B\times C}$ onto $(A^{B})^{C}$      II.5.2 R.4.14
Canonical mapping of $E\times F$ onto $F\times E$      R.3.4
Canonical mapping of $E\times F\times G$ onto $(E\times F)\times G$, etc.      R.3.12
Canonical mapping of $E_{\beta}$ into $\lim\limits_{\rightarrow}E_{\alpha}$      III.7.5 R.6.13
Canonical mapping of $F^{A}$ onto $\prod\limits_{i\in I}F^{A_{i}}$ (where $A=\bigcup\limits_{i\in I}A_{i}$, and $A_{i}\cap A_{\varkappa}\neq{\o}$ whenever $i\neq\varkappa$)      R.4.15
Canonical mapping of $F^{E}$ onto $\mathscr{F}(E,F)$      II.5.2
Canonical mapping of $\lim\limits_{\leftarrow}E_{\alpha}$ into $E_{\beta}$      III.7.1 R.6.14
Canonical mapping of $\mathscr{F}(B\times C,A)$ onto $\mathscr{F}(B,\mathscr{F}(C,A))$      II.5.2
Canonical mapping of $\prod\limits_{i\in I}X_{i}$ onto $(\prod\limits_{i\in J_{\alpha}}X_{i})\times(\prod\limits_{i\in J_{\beta}}X_{i})$($(J_{\alpha},J_{\beta})$ a partition of I)      II.5.5
Canonical mapping of $\prod\limits_{i\in I}X_{i}$ onto $\prod\limits_{\lambda\in L}(\prod\limits_{i\in J_{\lambda}}X_{i})$      II.5.5 R.4.11
Canonical mapping of $\prod\limits_{i\in I}X_{i}^{E}$ onto $(\prod\limits_{i\in I}X_{i})^{E}$      R.4.13
Canonical mapping of $\prod\limits_{i\in \{\alpha,\beta,\gamma\}}X_{i}$ onto $X_{\alpha}\times X_{\beta}\times X_{\gamma}$      II.5.3
Canonical mapping of $\prod\limits_{i\in \{\alpha,\beta\}}X_{i}$ onto $X_{\alpha}\times X_{\beta}$      II.5.3
Canonical mapping of $\prod\limits_{i\in \{\alpha\}}X_{i}$ onto $X_{\alpha}$      II.5.3
Canonical mapping of (E/S)/(R/S) onto E/R      II.6.7 R.5.9
Canonical mapping of a subset of E into E      II.3.7 R.2.3
Canonical mapping of an inverse limit into an inverse limit obtained by restriction of the index set      III.7.1
Canonical mapping of E onto E/R      II.6.2 R.5.2
Canonical mapping of G onto $\overset{-1}{G}$ (G a graph)      II.3.7
Canonical mapping, symmetry      R.3.4
Cantor's theorem      III.3.6
Cardinal of a set      III.3.1
Cardinal sum      III.3.3
Cardinal, dominant      III.6..Ex.21
Cardinal, finite      III.4.1
Cardinal, inaccessible      III.6..Ex.22
Cardinal, product      III.3.3
Cardinal, regular      III.6..Ex.17
Cardinal, singular      III.6..Ex.17
Cardinal, strongly inaccessible      III.6.Ex.22
Chain of an element in an ordered set (with respect to a mapping)      III.2.Ex.6
Characteristic function of a subset of a set      III.5.5
Characterization, typical      IV.1.4
Choice, axiom of      R.4.9
Class of objects equivalent to x (with respect to an equivalence relation)      II.6.9
Class, equivalence      II.6.2 R.5.2
Closed interval      III.1.13 R.6.4
Closure (mapping of an ordered set into itself)      III.1.Ex.13
Coarser equivalence relation      II.6.7
Coarser equivalence relation, preordering      III.1.4
Coarser equivalence relation, structure      IV.2.2
Coefficient, binomial      III.5.8
Cofinal subset      III.1.7 R.6.5
Coincidence (of two functions on a set)      II.3.5 R.2.14
Coinitial subset      III.1.7 R.6.5
Collectivizing relation      II.1.4
Commutativity (of union and intersection)      R.1.14
Comparable elements      III.1.12
Comparable structures      IV.2.2
Compatibility, of a function with two equivalence relations      II.6.5 R.5
Compatibility, of a relation with an equivalence relation      II.6.5 R.5.7
Complement of a set      II.1.7 R.1.7
Complete lattice      III.1.Ex.11
Complete solution      I.5.2
Completely ramified (ordered set)      III.2.Ex.8
Completion of an ordered set      III.1.Ex.15
Composition, of mappings      R.2.11
Composition, of sets      R.3.10
Composition, of two correspondences      II.3.3
Composition, of two graphs      II.3.3
Conjunction of two relations      I.3.4
Connected components of a set with respect to a relation      II.6.Ex.10
Constant of a theory      I.2.1
Constant, auxiliary      I.3.3
Constant, function or mapping      II.3.4 R.2.3
Constituents of a set with respect to a relation      II.6.Ex.11
Construction, echelon      IV.1.1
Construction, formative      I.1.3
Contained in a set      II.1.2 R.1.12
Continuum Hypothesis      III.6.4
Continuum, power of      III.6.4
Contradictory axioms      R.8.6
Contradictory theory      I.2.2
Contravariant signed echelon type      IV.2.Ex.1
Coordinate (first, second) of an ordered pair      II.2.1
Coordinate function (first, second)      II.3.6
Coordinate function of index i      II.5.3
Coordinate functions, on a product of a family of sets      R.4.11
Coordinate functions, on a product of several sets      R.3.12
Coordinate functions, on a product of two sets      R.3.1
Corollary      I.2.2
Correspondence defined at an object x      II.3.1
Correspondence denned by a relation      II.3.1
Correspondence, between two sets      II.3.1
Correspondence, inverse      II.3.2
Correspondence, one-to-one      II.3.7 R.2.9
Correspondences, composition of      II.3.3
Countable set      III.6.4 R.7.7
Countable union, intersection, product      R.7.9
Covariant signed echelon type      IV.2.Ex.1
Covering      II.4.6 R.4.4
Covering of a set      II.4.6
Covering, finer      II.4.6
Criterion of deduction      I.3.3
Criterion of substitution      I.1.2
Criterion, deductive      I.2.2
Criterion, formative      I.1.4
Critical ordinal      III.6.Ex.13
Decent set      III.2.Ex.20
Decimal system      III.5.7
Decomposition, canonical      II.6.5 R.5.3
Decreasing family of subsets      III.1.5 R.6.12
Decreasing mapping      III.1.5 R.6.12
Deduced (structure)      IV.1.6
Deduction, criterion of      I.3.3
Deduction, procedure      IV.1.6
Deductive criterion      I.2.2
Definition      I.1.1
Degree of disjointness of a covering      III.6.Ex.25
Demonstrative text      I.2.2
Descending induction      III.4.3
Diagonal mapping, of A into $A\times A$      II.3.7 R.3.4
Diagonal mapping, of E into $E^{I}$      II.5.3
Diagonal, of $A\times A$      II.3.3 R.3.4
Diagonal, of $E^{I}$      II.5.3
Diagrams      R.2.2
Difference of two integers      III.5.2
Different from      I.5.1
digit      III.5.7
Direct image of a structure      IV.2.6
Direct limit, of a direct system of mappings      III.7.6 R.6.13
Direct limit, of a direct system of sets      III.7.5 R.6.13
Direct system, of mappings      III.7.6 R.6.13
Direct system, of sets      III.7.5 R.6.13
Direct system, of subsets      III.7.6
Directed (left, right)      III.1.10 R.6.8
Directed with respect to the relation $\leqslant$      III.1.10
Disjoint segments      I.App.1
Disjoint sets      II.4.7 R.1.13
Disjunction, of cases, method of      I.3.3
Disjunction, of two relations      I.1.3
Distributive lattice      III.1.Ex.16
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