blocks of finite groups
Transfer in Hochschild Cohomology of Blocks of Finite Groups
... induces an isomorphism H ∗ (G, O) ∼ = H ∗ (H, O) by the “p−local” characterization of the cohomology rings. By Mislin’s theorem [15], the converse of this last statement is true, too, and in fact, a major guideline for ...
30
Rationality of blocks of quasi-simple finite groups
... the blocks of the finite groups of Lie type up to Morita equivalence, it is enough to parametrise the quasi-isolated ...of blocks of finite groups of Lie type for good ` had been ...
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Rationality of blocks of quasi-simple finite groups
... of finite reductive groups in character- istic different from ...for blocks of the finite groups of Lie type in non-defining characteristic in Section 5; the remain- ing cases in type E ...
24
Local control in fusion systems of p-blocks of finite groups
... Note added in proof: Since this work was written, a related result of M. Lechuga (Theorem 7.11 in his thesis Contribution ` a l’´etude locale dans les groups finis, Publ. Math. Univ. Paris 7, tome IV, 1994) has ...
20
Trivial source bimodule rings for blocks and p-permutation equivalences
... are blocks of finite groups G, H such that the block algebras OGb, OHc are Morita equivalent via an OGb-OHc-bimodule M with endo-permutation source V , then by a result of Puig [24], b and c have ...
35
On equivalences for cohomological Mackey functors
... of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived equivalence between two blocks induces a ...
11
Lusztig induction and ℓ-blocks of finite reductive groups
... of finite groups to questions about quasi-simple ...quasi-simple groups of Lie type form the by far most important ...these groups is thus of paramount importance for an eventual proof of ...
27
On blocks of strongly p-solvable groups
... The structure of the source algebras of blocks of p-solvable finite groups has been completely determined by Puig. Once the stated equality of Brauer categories is estab- lished (using Glauberman’s ...
8
Crossover morita equivalences for blocks of the covering groups of the symmetric and alternating groups
... ˆ finite groups and let b and c be central idempotents of F G and F G ˆ respectively such that F Gb and F Gc ˆ are split semi-simple ...a finite dimensional (F Gb, F Gc)-bimodule ˆ X, we will denote ...
17
Descent of Equivalences and Character Bijections
... of finite groups can be easily seen to be an extension of a p-permutation equivalence between the corresponding blocks over the subring of Witt ...
30
Character expansiveness in finite groups
... a finite group G is conjugacy expansive if for any normal subset S and any conjugacy class C of G the normal set SC consists of at least as many conjugacy classes of G as S ...
9
On the total character of finite groups
... Further, the above theorem was used by the authors in [19] to classify all the nonabelian p-groups of order p 4 (p an odd prime) which have a Johnson polynomial. The purpose of this article is to examine the ...
21
Conjugate factorizations of finite groups
... Observe that n ≤ | X | + ( | X 2 | − | X | ) + . . . + ( | X n | − | X n − 1 | ) = | X n | ≤ | G | hence | X | G | | = | X n | . Since 1 ∈ X | G | , X | G | ⊆ X 2 | G | and from | X | G | | = | X n | = | X 2 | G | | we ...
10
On some invariants of finite groups
... All groups considered here are finite. Our notation will be standard, and similar to that in [5]. By an invariant of a group G we mean a nonnegative integer, say α(G), chosen in such a way that G ' H ...
7
Finite BCI-groups are solvable
... a finite group and S and T are two subsets of G both of which contain the identity, then Cay(G, S \ { 1 } ) ∼ = Cay(G, T \ { 1 } ) implies that BCay(G, S) ∼ = BCay(G, T ...two groups, S ⊆ G, T ⊆ H, 1 G ∈ S ...
6
Sylow multiplicities in finite groups
... to profinite groups. It seems that the answer to this question is quite satisfactory: All of the major concepts and results which were so far examined from this perspective, have natural analogs for profinite ...
8
Algorithms for polycyclic by finite groups
... Tables 6.1–6.5 all follow the same format; the first and second columns of each table give the order (or in some cases, the structure) of the polycyclic normal sub- group, N , and the finite quotient, Q, ...
256
On metacyclic subgroups of finite groups
... The recovery of information about the structure of a finite group from information about its sub- groups has a long history. This survey article is intended to present some contributions in this context, ...
5
Symmetric generation of finite groups
... CHAPTER TWO: SYMMETRIC REPRESENTATION OF L 2(ll) ELEMENTS Introduction ... 25[r] ...
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Computing automorphism groups and isomorphism testing in finite groups
... To determine ∆ (7.1) in practice, we will need to construct a manageable representa- tion of Aut(R). As discussed in earlier chapters, computing representations of large automorphism groups is often impractical, ...
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