1216q(G, V) (cubic module parameter), 85
Q(G, V) (q ~ 2 offenders), 178
Q.(G, V), 178
U(X), 112
kerA(B), 113
Ai (fundamental weight of Lie type group),
386
( ... ) (subspace spanned by), 197
~ (ordering on 1-l(T) and M(T)), 61
~ (ordering on FF*-offenders), 68
11'(X) (primes dividing), 20
Baum(H) (Baumann subgroup), 75
r(G,T,A), 209
e(G) (for any odd prime p), 556
e(H) (generated by elements of order 3), 51
a(X, W) (module parameter), 232
b(r, V), 313
d(p), 347
e(G) (maximum 2-local p-rank), 4, 482
es (set as vector in permutation module), 83
gp(a) (universal completion), 265
m(X, W) (module parameter), 231
mp(M), 482
mp(M) (p-rank), 4
m2,p(G), 26
n'(X), 239
n(G), 210
p-rank, 4, 482
p1+2 (extraspecial of exponent p), 25
q(G, V) (quadratic module parameter), 67
qI+2w (special group of this order), 262
qrc-lemma, 177
r(G, V) (weak closure parameter), 231
r A, v (action ratio parameter), 67
s(G, V) (weak closure parameter), 232
w-offender (weak closure), 236
w(G, V), 236
A(X)(maximal rank elementary), 74
A^2 (G) (elementary 2-subgroups), 67
Aj(H) (corank j in maximal), 74
Ak(X, W) (for a-parameter), 232
B2(G) (2-radical subgroups), 121
C-component, 8, 41
C(G) (C-components), 41
£i, 210
£(G,T,A), 209
£i(G,T,A), 210
Q(S), 126
1-l ("partial " 2-locals), 500
7-l(X), 500
1-l(X, Y), 500
7-le, 499
7-le(X), 500
1-le(x, Y), 500
1-l.(T, M), 571
1-l'Q, 499
1-lv(T), 61
INDEXJC (known simple groups), 4, 482
JC-group, 4, 482
.C(G, T), 507
.C(H, S), 505
.C*(H,S), 505
.C1(G, T), 507
.Cj(G, T) (nonsolvable uniqueness groups),
507
M (maximal 2-locals), 499
M(X), 499
P(G, V) (FF*-offenders), 68
'P*(G, V), 68
Pa (FF-offenders), 76
'PR,G, 77
Q(G, V) (q ~ 2 offenders), 178
R2(G) (2-reduced subgroups), 77
S2(G) (2-subgroups), 121
Si(G), 500
U(X), 112
X (set including .C and B), 58
Xf, 59
(CPU) pushing up hypothesis, 122
(E) even characteristic hypothesis, 4, 482
(F-1)-module, 68
(F-1)-offender, 68
(F-j)-module, 256
(K) inductive "known" hypothesis, 4, 482
(PU) pushing up hypothesis, 122
(QT) quasithin hypothesis, 4, 482
(SQT) strongly quasithin, 32
(SQTK) strongly quasithin JC-group,. 33
V1M(X, 2) (invariant 2-subgroups), 56
2-component, 414
2-layer, 414
2-local p-rank, 26
2-radical, 121
2-reduced, 77, 491
2-signalizers, 56
2-stubborn, 121
2F-modules, 10
5-dimensional module for A5, 885AxB Lemma (Thompson), 24
almost special (group), 333
almost-extraspecial 2-group, 357
Alperin, J., 416, 518
Alperin-Brauer-Gorenstein Theorem (semidi-
hedral and wreathed Sylow 2-subgroups),
416
Alperin-Goldschmidt conjugation family, 518
Alperin-Goldschmidt Fusion Theorem, 519
amalgam, 14
amalgam (rank-2), 260
amalgam method, 6, 311
amalgam, subgroup, 260
Andersen, H., 329
apartment (of a rank-2 amalgam), 274
Aschbacher block, 123