On the Vertices of Irreducible Modules

Induction of Characters and p-Subgroups

“…In fact, we only need γ to be the product of a character of p -degree together with a "p-special" character. In particular, Theorem A holds whenever γ has degree not divisible by p (and this is the p-solvable case of a not so well-known consequence of some deep results of R. Knörr [7]). The following consequence of Theorem A seems, perhaps, surprising.…”

“…This is a not so well-known consequence of the deep results in [7]. If we do not assume that γ is p-factorable, Theorem 3.4 is also false.…”

The Alperin Weight Conjecture and Uno's Conjecture for the Baby Monster B, p Odd

“…Suz:2 as constructed in [14], and convert it into permutations on 3 13 4 × 2), being the normalizer of a 3B-pure 3 2 generated by the centre and one other element of 3 1+8 . We then go to work in the centralizer of an S 4 to find an element swapping the two generators for the 3 2 .…”

Contributions to Modular Representation Theory of Finite Groups

“…Since P is elementary abelian of order 25, assertion b) follows immediately from Knorr's theorem, see [55]. Assertion c) is an easy consequence of the group structure of N explained in the Atlas [18] Proof.…”