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Testing Modules of Groups of Even Order for Simplicity

✍ Scribed by Gerhard O. Michler; Øyvind Solberg

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
163 KB
Volume
202
Category
Article
ISSN
0021-8693

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✦ Synopsis

In this paper we exhibit an intimate relationship between the simplicity of an FG-module V of a finite group G generated by a noncentral involution t / 1 and Ä 4 some other element u in G and the socles of the eigenspaces E for in y1, 1 of Ž . the involution t considered as FC-modules, where C s C t is the centralizer of t G in G. In fact the two main results yield new simplicity criteria for FG-modules V over fields F with odd or even characteristic p, respectively. For p / 2 the result follows from a general module theoretic simplicity test proved in the first section of the paper. It builds on ideas of the Meat-axe algorithm of previous work. We show the practicability of our new tests by examples. ᮊ 1998 Academic Press * The authors have been supported by the European TMR-project Contract CHRX-CT94-0601 and the DFG research project ''Algorithmic Number Theory and Algebra.

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