Aschbacher M. — Finite Group Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Aschbacher M. — Finite Group Theory

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Название: Finite Group Theory

Автор: Aschbacher M.

Аннотация:

Finite Group Theory is intended to serve both as a text and as a basic reference on finite groups. In neither role do I wish the book to be encyclopedic, so I've included only the material I regard as most fundamental. While such judgments are subjective, I've been guided by a few basic principles which I feel are important and should be made explicit.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 274

Добавлена в каталог: 01.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$Aut_{G}(X)$       5
$A^{\theta}$       78
$B^{T}$       47
$B_{p}$ -Property      262
$Cyc_{g}$       54
$End_{R}(V)$       38
$E_{p^{n}}$       5
$F^{n\times n}$       42
$G\ast H$       33
$G\times H$       4
$G^{(n)}$       27
$G^{+}$       97
$G^{\sharp}$       6
$G_{Y}$ , G(Y), $G^{Y}$       14
$Hom_{R}(U,V)$       38
$H\cong G$       2
$H\leq G$       2
$H\unlhd G$       3
$H\unlhd\unlhd G$       23
$H^{1}(G,V)$       67
$ker(\alpha)$       3
$L_{n}(G)$       28
$Mod_{p^{n}}$ , $D_{2^{n}}$       107
$m_{2,p}(G)$       260
$m_{p}(G)$       5
$M_{X}(g)$       43
$N^{K}_{F}$       84
$N_{G}(X)$ , $C_{G}(X)$       3 14
$n_{p}$ , $|G|_{p}$       19
$n_{\pi}$ , $|G|_{\pi}$       71
$O^{\varepsilon}_{n}(q)$ , $SO^{\varepsilon}_{n}(q)$       89
$O_{p^{'},E}(G)$       159
$O_{\infty}(G)$       158
$O_{\pi}(G)$ , $O^{\pi}(G)$       5
$PO^{\varepsilon}_{n}(q)$ , $P\Omega^{\varepsilon}_{n}(q)$       89
$PSL_{n}(F)$ , $PGL_{n}(F)$       44
$PSp_{n}(q)$ , $PGU_{n}(q)$       89
$p^{1+2n}$ , $D^{n}_{8}Q^{m}_{8}$       110 111
$SD_{2^{n}}$ , $Q_{2^{n}}$       107
$SL_{n}(F)$ , $L_{n}(F)$       44
$Sp_{n}(q)$ , $SU_{n}(q)$       89
$Syl_{p}(G)$       19
$U^{K}$ , $K\otimes F^{U}$       119
$V\otimes U$       118
$W(\Sigma)$       148
$x^{G}$       3
$Z_{n}(G)$       28
$\alpha |_{R}$       6
$\alpha^{G}$       187
$\alpha_{G}(B)$       175
$\Delta(V,f)$ , $\Delta(V,Q)$       78
$\Gamma(G,T)$       8
$\Gamma_{P,k}(G)$ , $\Gamma^{0}_{P,k}(G)$       246
$\mathbb{C}$ , $\mathbb{Q}$ , $\mathbb{R}$       6
$\mathbb{Z}_{n}$       4
$\mathscr{A}(G)$       162
$\mathscr{D}(X)$       244
$\mathscr{E}^{p}_{k}(G)$       245
$\mathscr{E}^{p}_{k}(G)^{0}$       245
$\mathscr{P}(G,V)$       163
$\Omega^{\varepsilon}_{n}(q)$       89
$\Omega_{n}(G)$ , $\Omega^{n}(G)$       5
$\perp$       76
$\Phi(H)$       105
$\pi$ -group      5
$\pi(G)$       5
$\pi^{K}$       119
$\pi^{\sigma}$ , $V^{\sigma}$       121
$\Pi_{i}G_{i}$       4
$\Sigma^{+}$       149
<S>      2
Algebraic integer      184
Alperin's Fusion Theorem      200
Alt(X)      55
Alternating group      54
Apartment      214
Aut(X)      7
Automizer      5
Automorphism      7
Baer — Suzuki Theorem      204
Bar convention      6
Basis, dual      47
Basis, hyperbolic      81
Basis, orthogonal      79
Basis, orthonormal      79
BN-pair      217
Borel subgroup      218
Brauer — Fowler Theorem      243
Building      214
Building Weyl group      218
Burnside $p^{a}q^{b}$ -Theorem      186
Burnside Normal p-Complement Theorem      202
Cartan subgroup      218
Category      6
Category, coproduct      7
Category, product      7
Cauchy's theorem      20
Central product      32
Central product with identified centers      33
centralizer      3
Chamber      208
char(G)      180
CHARACTER      49
Character table      182
Character, degree      179
Character, generalized      180
Character, induced      188
Character, irreducible      179
Characteristic value      127
Characteristic vector      127
cl(G)      179
Class function      178
Classical group      88
Classification Theorem      259
Clifford algebra      95
Clifford group      96
Clifford's theorem      41
Cocycle      64
Commutator      26
Comp(G)      157
COMPLEX      208
Complex, chamber      208
Complex, chamber graph      208
Complex, connected      208
Complex, reflection      211
Complex, thick      208
Complex, thin      208
Component theorem      263
Composition factors      24
Composition series      23
conjugate      3
Coprime Action Theorem      73
Covering      167
Coxeter complex      210
Coxeter diagram      142
Coxeter group      142
Coxeter matrix      141
Coxeter system      142
Coxeter system, irreducible      147
Critical subgroup      108
CYCLE      53
Cycle structure      53
Dihedral group      141
Direct product      4
Distance      8
Dual space      47
Dynkin diagram      250
E(G)      158
EDGE      8
Exact sequence      46

Exact sequence, short      46
Exact sequence, split      47
Exchange condition      144
Extension, central      166
Extension, perfect      167
Extension, universal      166
F(G)      158
F*(G)      159
FG-homomorphism      37
FG-representation      35
Field, perfect      92
Fitting subgroup      158
Fitting subgroup, generalized      159
Fix(S)      14
Fixed point      14
Flag      8
Folding      210
Folding, opposite      211
Form, bilinear      76
Form, equivalent      78
Form, hermitian symmetric      76
Form, nondegenerate      76
Form, orthogonal      76
Form, quadratic      77
Form, radical      76
Form, sesquilinear      75
Form, similar      78
Form, skew hermitian      104
Form, skew symmetric      76
Form, symmetric      76
Form, symplectic      76
Form, Witt index      78
Frattini argument      20
Frattini subgroup      105
Frobenius complement      190
Frobenius kernel      191
Frobenius Normal p-Complement Theorem      203
Frobenius reciprocity theorem      189
Frobenius' Theorem      191
Fusion, control      199
G-isomorphism      9
G-morphism      9
G/H      3
gallery      208
Gaschuetz' Theorem      31
General linear group      9
General unitary group      89
Geometry      8
Geometry, connected      8
Geometry, flag      8
Geometry, flag transitive      9
Geometry, morphism      8
Geometry, oriflamme      99
Geometry, polar      99
Geometry, rank      8
Geometry, residually connected      8
Geometry, residue      8
Geometry, type      8
GL(V)      9
Glauberman Z*-Theorem      261
Graph      8
Graph, connected      8
Graph, connected component      8
Group algebra      36
Group, center      5
Group, characteristic p-type      260
Group, characteristically simple      25
Group, class      28
Group, complement      29
Group, covering      167
Group, exponent      5
Group, extension      30
Group, free      138
Group, Frobenius      190
Group, k-connected      245
Group, k-generated p-core      246
Group, Lie type      249
Group, metacyclic      202
Group, nilpotent      28
Group, perfect      27
Group, representation by conjugation      11
Group, ring      36
Group, section      260
Group,solvable      27
Grp(Y:W)      140
H char G      25
Hall $\pi$ -subgroup      71
Hx, xH      3
Hyperbolic pair      80
Hyperbolic plane      80
Induction map      189
Inn(G)      11
Inner automorphism group      11
Integer, $\pi$ -part      71
Integer, p-part      19
Involution      5
Isometry      78
Isomorphism      7
J(G)      162
J(X,f)      78
Jordan — Hoelder theorem      24 37
Jordan's Theorem      58
k-group      260
L( $V_{1}$ ,..., $V_{m}$ ;V)      117
l(h), $l_{R}(h)$       143
Levi factor      256
Lie rank      249
Linear representation      9
Linear representation, absolutely irreducible      120
Linear representation, dual      47
Linear representation, enveloping algebra      42
Linear representation, indecomposable      37
Linear representation, induced      188
Linear representation, irreducible      37
Linear representation, irreducible constituents      37
Linear representation, principal      179
Linear representation, regular      182
Linear representation, tensor product      118
Linear representation, written over a field      124
Linear transformation, determinant      44
Linear transformation, m-linear      117
Linear transformation, nilpotent      128
Linear transformation, semisimple      127
Linear transformation, semisimple part      130
Linear transformation, trace      44
Linear transformation, unipotent      128
Linear transformation, unipotent part      130
LwrG, $Lwr_{\pi}G$       33
Maschke's Theorem      40
Maximal subgroup      5
Modular property of groups      6
Module, absolutely irreducible      120
Module, complement      37
Module, composition factor      37
Module, condensed      125
Module, cyclic      38
Module, extension      37
Module, homogeneous      40
Module, homogeneous component      40
Module, indecomposable      37
Module, irreducible      37
Module, permutation      50
Module, semisimple      38
Module, simple      37
Module, socle      38
Module, split extension      38
Morphism      6
Mov(A)      54
Normal p-complement      202
Normal series      20

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