Index Page locations for definitions, as well as for references which are particularly fundamental, are indicated in boldface. ∗ (asterisk), as central product H ∗ J of groups, 260 as join K ∗ L of simplicial complexes, 35 (5-point star), point as topological space, 238 :=, (initial) definition, 11 bydef = , by (earlier) definition, 11 ∼, isomorphism, 26 , as homotopy f g of maps, 105 as homotopy equivalence of spaces, 109 G , as G-homotopy f g of maps, 138 as G-homotopy equivalence of spaces, 138 ≤, as dominance relation f ≤ g on poset maps, 107 as inclusion A ≤ B of subgroups, 13 as order relation x ≤P y in a poset P, 10 , notation for normal subgroup, 16 | − |, as geometric realization of a poset, 26 of a simplex via convex hull of vertices, 24 of a simplicial complex, 24 as order of a group, 3, 15 | − |p, p-part of group order, 15 An, alternating group, 41, 42, 189, 233, 292 A5, 39, 87, 158, 178, 185, 202, 209, 210, 215–217 isomorphisms, see also L2(4), Ω−(2) 4 A6, 86, 90, 91, 93–96, 158, 216, 323 isomorphism, see also Sp4(2) 3A 6 , nonsplit triple cover of A 6 , 86, 93 A 7 , 88, 211, 293, 294 C3-geometry for —, 90, 91, 92, 133, 158, 179, 210, 218, 234, 255, 272, 292, 294, 303, 305, 320, 323–325 A8, 39, 218, 323 isomorphisms, see also L4(2), Ω + 6 (2) Abels, H. -Abramenko, subcomplexes of buildings [AA93] , 302 Abramenko, P. Abels- —, subcomplexes of buildings [AA93] , 302 -Brown, buildings book (expanded) [AB08] , 43, 59, 292 abstract characteristic p, 85 minimal parabolic subgroup, 286 simplex, 18 simplicial complex, 18 action, 28 admissible —, 30 coprime —, 191, 263, 266 faithful —, 265 flag-transitive, 46, 49, 53, 55, 58, 71, 83, 115, 233, 234, 245, 253, 293, 327, 328 free —, 180 type-preserving —, 30 acyclic, 176 carrier, 144 Acyclic Carrier Theorem, 144 Adem, A., xi, 5, 234, 235 -Maginnis-Milgram, cohomology of M12 [AMM91] , 235, 236, 256, 304 -Milgram, cohomology of M22 [AM95a], 204, 235 -Milgram, cohomology of McL [AM97], 235 -Milgram, group cohomology book [AM04] , 103, 155, 159, 205, 225, 228, 234, 235, 239, 243 -Milgram, rank 3 groups have Cohen-Macaulay cohomology [AM95b] , 304 admissible action, 30 aﬃne building, 81, 88, 92, 272, 292, 292, 293, 302 Dynkin diagram, 81, 92, 292, 293 345

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