Solomon's induction in quasi-elementary groups

Details Solomon's induction in quasi-elementary groups Solomon's induction in quasi-elementary groups

2010-06-30

arxiv.org/abs/1006.5752v1

Mathematics

Group Theory

2 pages, to appear in J. Group Theory

Scientific paper

Given a finite group G, we address the following question: which multiples of the trivial representation are linear combinations of inductions of trivial representations from proper subgroups of G? By Solomon's induction theorem, all multiples are if G is not quasi-elementary. We complement this by showing that all multiples of p are if G is p-quasi-elementary and not cyclic, and that this is best possible.

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