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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.

Аннотация:

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Distributivity, of union and intersection of a family of sets      R.4.3 R.4.8
Distributivity, of union and intersection of two sets      R.1.14
Divergent mapping (of an ordinal into itself)      III.6.Ex.23
Divisible by an integer      III.5.6
Division of an integer      III.5.6
Division, Euclidean      III.5.6
Domain, of a correspondence      II.3.1
Domain, of a graph      II.3.1
Dominant cardinal      III.6.Ex.21
Double family      II.3.4
Double sequence      III.6.1 R.7.8
Dual formulae      R.1.15 R.4.7
Duality rule      R.1.15 R.4.7
Dyadic system      III.5.7
E/R (E a set, R an equivalence relation on E)      R.5.2
E/R (E a set, R an equivalence relation)      II.6.2
Echelon type      IV.1.Ex.1
Echelon, echelon construction, echelon construction scheme      IV.1.1
Echelon, signed      IV.2.Ex.1
Element      II.1.1
Element, fixed (under a mapping or set of mappings)      R.2.3
Element, generic      R.1.2
Element, greatest      III.1.3 R.6.5
Element, invariant (under a mapping or set of mappings)      R.2.3
Element, least      III.1.3 R.6.5
Element, maximal      III.1.6 R.6.6
Element, minimal      III.1.6. R.6.6
Elements, comparable      III.1.12
empty function      II.3.4
Empty set      II.1.7 R.1.8
Empty word      I.App.1
Endowed with a structure      IV.1.4
Endpoints of an interval      III.1.13 R.6.4
Eq (X,Y), Card (X)      III.3.1
equal      I.5.1
Equalitarian theory      I.5.1
Equality, relation of      I.5.1 R.1.6
equation      I.5.2
Equipotent sets      III.3.1 R.7.1
Equivalence class      II.6.2 R.5.2
Equivalence relation      II.6.1 R.5.2
Equivalence relation on a set      II.6.1
Equivalence relation, associated with a function      II.6.2
Equivalence relation, coarser      II.6.7
Equivalence relation, finer      II.6.7
Equivalence relation, induced      II.6.6
Equivalence relation, product      II.6.8
Equivalence relation, quotient      II.6.7
Equivalence, on a set      II.6.1
Equivalent axioms      R.8.4
Equivalent elements      II.6.1
Equivalent powers      R.7.2
Equivalent relations      I.3.5 R.1.3
Equivalent species of structures      IV.1.7
Equivalent theories      I.2.4
Euclidean division      III.5.6
Even integer      III.5.6
Existential quantifier      I.4.1
Expansion of an integer to base b      III.5.7
Explicit axiom      I.2.1
exponentiation      R.4.9
Extension of a correspondence or mapping to sets of subsets      II.5.1 R.2.4
Extension of a family of functions to product sets      II.5.7
Extension of a mapping      II.3.5 R.2.13
Extension of an ordering, order relation, preordering, preorder relation      III.1.4 R.6
Extension of several mappings to the product sets      R.3.14
Extension of two functions to product sets      II.3.9
Extension, canonical      IV. 1.2
Extension, inverse (of a mapping to sets of subsets)      R.2.6
Extent, axiom of      II.1.3
f(X) (X a subset)      R.2.4
f(x), $f_{x}$ (f a function), F(x), $F_{x}$ (F a functional gaph)      II.3.4
f(x), $f_{x}$, $x\rightarrow f(x)$ (f a mapping, x an element)      R.2.2
f(x,y), f(.,y), f(x,.), f( ,y), f(x, )      II.3.9
f: $A\rightarrow B$, $A\xrightarrow{f} B$      II.3.4
Factor, of a product      II.2.2 II.5.3
Factor, of an integer      III.5.6
Factorial n      III.5.8
Factorization of a mapping      R.2.11
Factorization, canonical      R.5.3
Factors, of a product set      R.3.1 R.4.9
False relation      I.2.2
Family      II.3.4
Family of elements of a set      II.3.4 R.2.14
Family of mutually disjoint sets      II.4.7
Family of subsets of a set      II.3.4
Family of subsets, decreasing (increasing)      III.1.5
Family, double      II.3.4
Family, finite      III.4.1
Final character (of a totally ordered set)      III.6.Ex.16
Final segment of a word      I.App.1
Final structure      IV.2.5
Finer covering      II.4.6
Finer preordering      III.1.4
Finer relation      II.6.7
Finer structure      IV.2.2
Finite cardinal      III.4.1
Finite character (property of, set of subsets of)      III.4.5 R.6.11
Finite family      III.4.1
Finite sequence, finite sequence of elements of a set      III.5.4 R.7.8
Finite set      IV.4.1
First coordinate of an ordered pair      II.2.1
First projection of a graph      II.3.1
First species      I.1.3
First term of a sequence      III.5.4
Fixed element      II.3.4 R.2.3
Formative construction      I.1.3
Formative criterion      I.1.4
Free subset of an ordered set      III.1.Ex.5
Function      see "Mapping"
Function of several variables      R.3.13
Function of two arguments      II.3.9
Function, characteristic      III.5.5
Function, coordinate      II.3.6 II.5.3
Function, defined on A with values in B      II.3.4
Function, not depending on x      II.3.9
Functional graph      II.3.4
Functional relation      I.5.3 R.2.1
Functional symbol      I.5.3
G<X>, G(X), G(x) (G a graph, X a set, x an object)      II.3.1
General solution      I.5.2
General term (of a sequence)      R.7.8
Generalized Continuum Hypothesis      III.6.4
Generic element (of a set)      R.1.2
Generic Structure      IV.1.4
gf (g,f mappings) (by abuse of language)      II.3.7
Graph      II.3.1
Graph of a correspondence      II.3.1
Graph of a mapping      R.3.5
Graph of a relation      II.3.1 R.3.2
Graph symmetric      II.3.2
Graph, functional      II.3.4
Graph, inverse      II.3.2
Graphs, composition of      II.3.3
greater      III.1.3 R.6.3
Greatest element of an ordered set      III.1.7 R.6.5
Greatest lower bound      III.1 R.6.7
Half-open interval      III.1.13 R.6.4
Hypothesis, auxiliary      I.3.3
Hypothesis, continuum      III.6.4
Hypothesis, generalized continuum      III.6.4
Hypothesis, inductive      III.2.2 III.4.3
Identification      R.8.5
Identity      R.1.3
Identity correspondence      II.3.3
Identity mapping      II.3.4 R.2.3
Image of a covering      II.4.6
Image of a function (by abuse of language)      R.2.4
Image of a set      II.3.2
Image of a set under a correspondence      II.3.1
Image of a set under a function      II.3.4 R.2.4
Image of a set under a graph      II.3.1
Image of an equivalence relation      II.6.6
Image, direct (of a structure)      IV.2.6
Image, inverse (of a set under a mapping)      R.2.6
Image, inverse (of a structure)      IV.2.4
Implicit axiom      I.2.1
IMPLY      R.1.3
Inaccessible cardinal      III.6.Ex.22
Inaccessible initial ordinal      III.6.Ex.16
Inclusion relation      II.1.2 III.1.1 R.1.2
Inconsistent axioms      R.8.6
Increasing family of subsets      III.1.5 R.6.12
Increasing mapping      III.1.5 R.6.12
Indecomposable ordinal      III.2.Ex.16
Independent (of other axioms)      I.2.Ex.1
Index set of a family      II.3.4 R.2.2
Indicial notation      R.2.2
Induced equivalence relation      R.5.5
Induced mapping      II.6.5
Induced ordering, order relation, preordering, preorder relation      III.1 R.6.1
Induced relation      II.6.3
Induced structure      IV.2.4
Induction, descending      III.4.3
Induction, Noetherian      III.6.5
Induction, Principle of      III.2.2 III.4.3
Induction, restricted      III.4.3
Induction, starting at k      III.4.3
Induction, transfinite      III.2.2
Inductive hypothesis      III.2.2 III.4.3
Inductive set      III.2.4 R.6.9
Infimum      III.1.9 R.6.7
Infinite sequence      III.6.1 R.7.8
Infinite set      III.6.1
Infinity, axiom of      III.6.1
Initial ordinal      III.6.Ex.10
Initial segment of a word      I.App.1
Initial structure      IV.2.3
Injection      II.3.7 R.2.8
Injection, canonical      II.3.7
Injective mapping      II.3.7 R.2.8
Integer, natural      III.4.1
Integral part of the quotient of two integers      III.5.6
Intersecting subsets      R.1.13
Intersection of a family of sets, or subsets      II.4.1 R.4.6
Intersection of a set of sets      II.4.1
Intersection of several sets      R.1.13
Intersection, countable      R.7.9
Intervals (closed, half-open, open, unbounded)      III.1.13 R.6.4
Intransitive      II.6.Ex.11
Intrinsic term      IV.1.6
Invariant element      R.2.3
Inverse extension of a mapping      R.2.6
Inverse image      R.2.6
Inverse image of a covering      II.4.6
Inverse image of a set      II.3.2
Inverse image of a structure      IV.2.4
Inverse image of an equivalence relation      II.6.6
Inverse isomorphisms      IV.1.5
Inverse limit, of a family of mappings      III.7.2 R.6.14
Inverse limit, of a family of sets      III.7.1 R.6.14
Inverse system, of mappings      III.7.2 R.6.14
Inverse system, of sets      III.7.1 R.6.14
Inverse system, of subsets      III.7.2
Inverse, of a (bijective) mapping      II.3.7 R.2.9
Inverse, of a correspondence      II.3.2
Inverse, of a graph      II.3.2
Involutory permutation      II.3.7 R.2.9
Irreducible element (of a lattice)      III.4.Ex.7
Isomorphic sets      IV.1.5
Isomorphic structures      IV.1.5 R.8.6
Isomorphism      IV.1.5 R.8.6
Isomorphism of ordered sets      III.1.3
Iterates of a mapping      III.6.2 R.2.11
K(X) (K a subset of $E\times F$, X a subset of E)      R.3.6
K(x) (K a subset of $E\times F$, x an element of E)      R.3.9
Larger than      III.1.3
Last term of a finite sequence      III.5.4
Lattice      III.1.11 R.6.8
Lattice, Boolean      III.1.Ex.17
Lattice, complete      III.1.Ex.11
Lattice, distributive      III.1.Ex.16
Lattice, relatively complemented      III.1.Ex.17
Least element of an ordered set      III.1.7 R.6.5
Least upper bound      III.1.9 R.6.7
Least upper bound of a family of cardinals      III.3.2
Left directed set      III.1.10 R.6.8
Left inverse (of an injection)      II.3.8
Left-hand endpoint of an interval      III.1.13
Legitimation, theorem of      I.3.3
Lemma      I.2.2
Lemma, Zorn's      III.2.4 R.6.10
Length, of a finite sequence      III.5.4
Length, of a word      I.App.1
Less than      III.1.3 R.6.3
Lexicographical order relation, ordering      III.2.6
Lexicographical product      III.2.6 III.2.Ex.10
Limit, direct      III.7.5 R.6.13
Limit, inverse      III.7.1 R.6.14
Linearly ordered      see "Totally ordered"
Link      I.1.1
Logical components of a relation      I.App.Ex.6
Logical construction      I.App.Ex.6
Logical sign      I.1.1
Logical theory      I.3.1
Logically constructed      I.App.Ex.6
Logically irreducible      I.App.Ex.6
Lower bound      III.1.8 R.6.7
Lower bound, greatest      III.1.9 R.6.7
Mapping      R.2.1
Mapping of a set into a set      II.3.4
Mapping of a set onto a set      II.3.7
Mapping, bijective      II.3.7 R.2.9
Mapping, bounded above (bounded below, bounded)      III.1.8 R.6.7
Mapping, compatible with an equivalence relation      II.6.5
Mapping, compatible with two equivalence relations      R.5.8
Mapping, composite      II.3.7 R.2.11
Mapping, constant      II.3.4 R.2.3
Mapping, decreasing      III.1.5 R.6.12
Mapping, diagonal      II.3.7 II.5.3 R.3.4
Mapping, empty      II.3.4
Mapping, identity      II.3.4 R.2.3
Mapping, increasing      III.1.5 R.6.12
Mapping, injective      II.3.7 R.2.8
Mapping, inverse      II.3.7 R.2.9
Mapping, monotone      III.1.5
mapping, one-to-one      II.3.7 R.2.9
Mapping, order-preserving      III.1.5
Mapping, order-reversing      III.1.5
Mapping, partial      II.3.9 R.3.13
Mapping, strictly decreasing (strictly increasing, strictly monotone)      III.1 R.6.12
Mapping, surjective      II.3.7 R.2.4
Mapping, universal      IV.3.1
Mappings, agreeing on a set      II.3.5
Mappings, canonical      see "Canonical"
Mathematical theory      I.1.1 I.2.1 I.2.2
Maximal element      II.1.6 R.6.7
Maximum      R.6.5
Membership, relation of      II.1.1 R.1.10
Method, of disjunction of cases      I.3.3
Method, of reductio ad absurdum      I.3.3
Method, of the auxiliary constant      I.3.3
Method, of the auxiliary hypothesis      I.3.3
Minimal element      III.1.6 R.6.6
Minimum      R.6.5
Mobile (set of finite subsets)      III.4.Ex.11
Model of a theory      I.2.4
Monotone mapping      III.1.5
Morphism      IV.2.1
Multiple of an integer      III.5.6
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