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