Module correspondence in finite groups

ON p- SOLUBLE GROUPS AND THE NUMBER OF SIMPLE MODULES ASSOCIATED WITH A GIVEN BRAUER PAIR

“…with the Klilshammer-Puig generalisation [13, 1.20.3] of Dade's theorem [6,10] perhaps suggest the possibility of extending the machinery in this paper to reduce, to the almost simple cases, local assertions relating to Alperin [19], but [19,4.1] is actually the special case of Corollary 1.3(a) where P is a defect group of a. Corollary 13(a) is Okuyama [18,Theorem 5] (reference specifications indicate this undated typescript to have been written in 1980 or 1981). The last line of Okuyama's argument elides over the need to check that Dade's equivalence [6,10] can be chosen compatibly with the Brauer correspondence.…”

Monomial representations and generalizations

“…First we note [12] Monomial representations and generalizations 275 PROOF. Let &~ be the class of all finite groups whose composition factors all have abelian Sylow p-subgroups.…”

On Representation of Monomial Groups

“…T.Okuyanta [12] proved that if G is an M-group and P is Sylow P-subgroup of G, then ()/ G NPP is an M-group. I.M.Issacs [7] shows that if H is a Hall subgroup of an M-group then ()/ G NHH ′ is also and M-group.…”