This proposal extends much work done during the last funding period. Two topics, however, which have separate goals, have brief summaries in x10. Together they form documentation of the results that came from the funding period of NSF GRANT #9622928. 1. An outline of the main problems of this proposal Let G be a nite group. Call a conjugacy class C a p 0-class if its elements have order prime t...

Each finite p-perfect group G (p a prime) has a universal central p-extension coming from the p part of its Schur multiplier. Serre gave a StiefelWhitney class approach to analyzing spin covers of alternating groups (p = 2) aimed at geometric covering space problems that included their regular realization for the Inverse Galois Problem. A special case of a general result is that any finite simp...

Each finite p-perfect group G (p a prime) has a universal central p-extension coming from the p part of its Schur multiplier. Serre gave a StiefelWhitney class approach to analyzing spin covers of alternating groups (p = 2) aimed at geometric covering space problems that included their regular realization for the Inverse Galois Problem. A special case of a general result is that any finite simp...

∗ We initiate a study of the rings of invariants of modular representations of elementary abelian p-groups. With a few notable exceptions, the modular representation theory of an elementary abelian p-group is wild. However, for a given dimension, it is possible to parameterise the representations. We describe parameterisations for modular representations of dimension two and of dimension three....

This paper is a sequel to Curtis [7], where the Held group was constructed using a 7-modular monomial representation of 3·A7, the exceptional triple cover of the alternating group A7. In this paper, a 5-modular monomial representation of 2·HS:2, a double cover of the automorphism group of the Higman–Sims group, is used to build an infinite semi-direct product P which has HN, the Harada– Norton ...