Index
abelian Hall subgroup and 7r-length, 94
abelian normal subgroups all cyclic, 189
abelian Sylow subgroup intersection, 38
action, 1
action on cosets, 3, 148
action on subspaces of vector space, 228ff
action on right transversal, 148
action via automorphisms, 68
action, Frobenius, 177ff
action, semiregular, 177
actions fixing prime order elements, 141j(f
additive commutator in ring, 125
adjoint (classical) of matrix, 321
admit (of action), 131
Alperin, J., 55, 323
alternating group, 34
alternating group, definition, 326
alternating group, Schur multiplier of, 152
alternating group, simplicity of, 250
arrows in transitive action, 262
augmentation ideal, 315
augmentation map, 314
automorphism, definition, 334
automorphism of symmetric group, 33, 250
automorphism tower, 278
automorphism, order of, 70
axiom of choice, 333
Baer theorem, 55
Baer trick, 142
bar convention, 23
Bartels theorem, 290
base group of wreath product, 73
basis for free abelian group, 315
Bender, H., 31, 217, 271
Berkovich, Y., 86
binomial coefficient, 9
block (of action), 237
Bochert theorem, 246jJ
Brodkey theorem, 38, 71, 74
Burnside, book of, 181, 217
Burnside orbit count, 7
Burnside p
a
g
b
-theorem, 216j(f
Burnside p-nilpotence theorem, 159
Burnside theorem, prime degree action, 240
Burnside, W., 30
Cameron, P., 249, 285
canonical homomorphism, 338
Carter subgroup, 91
Cauchy theorem, 8, 10
Cauchy-Frobenius orbit count, 7
center of group, 2, 334
central extension, 151
central prime order elements, 174
central series, 20, 115
central subgroup, transfer to, 154
centralizer, definition, 339
Cermak-Delgado subgroup, 43
chain stabilizer, 137
character theory, 53, 59, 147, 182, 216-217
character, permutation, 236
characteristic series, 7r-separable, 92
characteristic subgroup, 11
characteristic subgroup, definition, 335
characteristically simple group, 277
Chermak-Delgado theorem, 41
class 2 group, 122, 142
class (conjugacy), 4
class equation, 5
class (nilpotence), 22, 116, 119
class size, 6
345
Previous Page Next Page