Bechtell H. — The theory of groups :: Электронная библиотека попечительского совета мехмата МГУ

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Bechtell H. — The theory of groups

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Название: The theory of groups

Автор: Bechtell H.

Язык:

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 144

Добавлена в каталог: 15.12.2004

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

Предметный указатель

$C_{p^\infty}$ , group      7 23
$C_{p^\infty}$ , properties of      23
$\pi$ -group      35
$\pi$ -group, properties of      35
$\pi$ -number      35
$\pi$ -subgroup      56
$\pi'$ -number      35 43
Abelian extension      87
Alternating group      6
Ascending central series      49 50
Ascending chain condition      71
Automorphism      4
Automorphism group      4
Automorphism group, of cyclic group      6
Automorphism group, of elementary abelian p-group      6
Automorphism, inner      4
Automorphism, outer      4
Baer      38
Basis Theorem      63
Bicyclic      90
Burnside      63 98 105
Burnside Basis Theorem      63
Category      123
Center      3
Central extension      87
centralizer      3
Characteristic series      49 61
Characteristic subgroup      4
Class equation      3
Commutator identities      53 55
Commutator subgroup      5
Complement      35
Complement, normal      98
Complement, p-      98
Composition series      5
conjugate      3
Conjugate subgroup      3
Coproduct element, category      131
Coproduct element, group      118
Coproduct object, category      131
Coproduct object, category, group      118
Coproduct, category      130 131
Coproduct, group      117
Core      71
Coset decomposition      1
Cyclic extension      87
Defining relations      114
Descending central series      50
Dihedral group      6 28
Direct factor      5 10
Direct product      5 10
Direct product with amalgamated subgroup      13
Direct product, properties of      11 12 16 55
Direct sum      10
Direct summands      10
Dixon      35—38
Double coset      101 102
Elementary abelian      6 46 48
Elementary commutator      66
Endomorphism      3
Epimorphism      3
Equivalent extension systems      81
Equivalent extensions      24 25 80—83 87
Exact sequence      23
Extension system      80
Extensions      23 76
Extensions of abelian groups      84
Extensions, abelian      87
Extensions, central      87
Extensions, cyclic      87
Extensions, splitting      26 83 88
Factor set      76
Factorizable      22
Fitting subgroup      67
Frattini subgroup      56 67
Free Abelian group      121
Free factors      115
Free generators      113
Free group      110 116
Free group object      111
Free product      115
Frobenius      106 107
Fully invariant subgroup      4
functor      125
Functor, contravariant      125
Functor, contravariant horn      126
Functor, covariant      125
Functor, hom      125
Gaschutz      38 39 40 64
Generalized quaternion group      91
Generating set      2 110
Generating set, minimal      63
Generator      56 110
Group $C_{p^\infty}$       7 23
Group, $\pi -$       35
Group, alternating      6
Group, bicyclic      9
Group, dihedral      6
Group, elementary abelian      6 46 48
Group, free      110 116
Group, free abelian      121
Group, generalized quaternion      91
Group, metacyclic      89 90 99
Group, nilpotent      5 50 53 54 74
Group, p-      5 26 51 52 56 64 84 90 91 92 93
Group, p-nilpotent      98 100 105—107 109
Group, p-normal      103 105
Group, periodic      5
Group, quaternion      6 66 75 80
Group, simple      5 99 107 109
Group, square-free order      42 100
Group, supersolvable      69 108
Group, symmetric      6
Group, symmetric of degree four      22 42 46 66
Group, torsion-free      5
Grun      102 103
Grun, theorems of      100
Hall $\pi$ -subgroup      43
Hall subgroup      43 104
Hall subgroup, properties of      43
Hall, P.      44 45 48 58
Hereditary property      65
Higman, D. G.      41

Holomorph      28
Homomorphism      3
Huppert      75
Hypercenter      49 50 55
Hypercommutator      49 50 55
Index relations      21 22
Injections      131
Invariant series      5 49 70 72
Invariant subgroup      4
Isomorphism      4
Isomorphism theorems      4
Ito      55 106
k-th roots      47
Kernel      4
Lower central chain      49
Lower central series      50
Lower central series, length of      50
Mappings      1
Mappings, bijective      1
Mappings, cartesian product of      1
Mappings, injective      1
Mappings, projection      1
Mappings, surjective      1
Maschke’s Theorem      47 48
Maximal condition      71
Metacyclic group      89 90 99 109
Minimal generating set      63
Modular identity      21
Monomorphism      3
Morphism      123
Nilpotent      5 50 53 54 74
Nongenerator      56
Normal complement      98
Normal series      5 49
Normal subgroup      3
normalizer      3
Order      2
Order, element      2
Order, group      2
Ore      39
p-commutator subgroup      100
p-complement      98
p-complement, normal      98
p-group      5 26 51 52 56 64 84 91 92 93
p-nilpotent      98 100 105—107 109
p-normal      103 105
Periodic group      5 39
Permutable subgroup      20
Permutably decomposable      22
Product element      9
Product in category      130 131
Product object      9 130 131
Product of groups      8
Product of subgroups      21
Projections      8 130
Quaternion group      6 66 75 80
Quotient group      3
Reduced product      41 64
Sah      54
Schreier      79
schur      38
Semidirect product      28
Semidirect product, representable as      28
Series, characteristic      49 61
Series, composition      5
Series, descending central      50
Series, invariant      5 49 70 72
Series, lower central      50
Series, normal      5 49
Series, upper central      49
Short exact sequence      23
Simple group      5 99 107 109
Sockel      69
Solvable group      5 45 46
Splits      28 37—41 66 98
Splitting extension      26 83 88
Subdirect product      16
Subdirect product, properties of      18 19
Subdirect product, representation as      16
Subgroups, $\pi-$       56
Subgroups, center      3
Subgroups, characteristic      4
Subgroups, commutator      5
Subgroups, conjugate      3
Subgroups, fully invariant      4
Subgroups, Hall      43 104
Subgroups, Hall $\pi -$       43
Subgroups, invariant      4
Subgroups, normal      3
Subgroups, p-commutator      100
Subgroups, permutable      20
Subgroups, subnormal      5
Subgroups, Sylow $\pi-$       39
Subgroups, Sylow p-      5 23 26 32 34 67
Subgroups, system normalizer      46
Subnormal $\pi$ -subgroup      56
Subnormal subgroup      5
Supersolvable groups      69 108
Sylow $\pi$ -subgroup      39
Sylow $\pi$ -subgroup, properties of      39 46
Sylow basis      45
Sylow p-subgroup      5 23 26 32 34 67
Sylow p-subgroup of symmetric group      32 34
Sylow p-subgroup, properties of      5 23 26
Sylow theorems      5
Symmetric group      6
System normalizer      46
Torsion-free group      5
TRANSFER      94
Universal element      127
Universal object      127
Upper central chain      49
Upper central series      49
Upper central series, length of      49
Van der Waerden      115
Von Dyck      114
Words      113 115
Wreath product      30
Wreath product, properties of      30
Wreath product, restricted      30
Wreath product, standard restricted      30
Wreath product, standard unrestricted      30
Wreath product, unrestricted      30
Zassenhaus      39 43

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