Rhetorical biset functors, rational p-biset functors and their semisimplicity in characteristic zero
Date
2008
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Source Title
Journal of Algebra
Print ISSN
0021-8693
Electronic ISSN
1090-266X
Publisher
Academic Press
Volume
319
Issue
9
Pages
3810 - 3853
Language
English
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Abstract
Rhetorical biset functors can be defined for any family of finite groups that is closed under subquotients up to isomorphism. The rhetorical p-biset functors almost coincide with the rational p-biset functors. We show that, over a field with characteristic zero, the rhetorical biset functors are semisimple and, furthermore, they admit a character theory involving primitive characters of automorphism groups of cyclic groups.