Editor-in-Chief: Wilson, John S.
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1Robinson College, Cambridge CB3 9AN, U.K.
Citation Information: Journal of Group Theory. Volume 14, Issue 1, Pages 49–51, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/jgt.2010.040, August 2010
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.
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