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Abstract
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 have this property 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.
Received: 2009-12-13
Revised: 2010-03-04
Published Online: 2010-08-13
Published in Print: 2011-January
© de Gruyter 2011
