✦ LIBER ✦

A Modular Version of Maschke′s Theorem for Groups with Cyclic p-Sylow Subgroups

✍ Scribed by M. Schaps

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 499 KB
Volume: 163
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1994.1034

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✦ Synopsis

We prove that the group algebra of a finite group with a cyclic p-Sylow subgroup over an algebraically closed field is a specialization of a parameter-dependent multiplication structure which gives a semisimple algebra for general values of the parameter. We actually prove the existence of such a specialization for any block of cyclic defect group. (\quad 1994) Academic Press. Inc.

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✍ Ian Hughes; Gregor Kemper 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 207 KB

Let V be a representation of a finite group G over a field of characteristic p. If p does not divide the group order, then Molien's formula gives the Hilbert series of the invariant ring. In this paper we find a replacement of Molien's formula which works in the case that G is divisible by p but not