The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2

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Abstract

For a finite group G, an L(G)-free gap G-module V is a finite dimensional real G-representation space satisfying the two conditions: (1) V L = 0 for any normal subgroup L of G with prime power index. (2) dim V P > 2 dim V H for any P < H ≤ G such that P is of prime power order. A finite group G not of prime power order is called a gap group if there is an L (G)-free gap G-module. We give a necessary and sufficient condition for that G is a gap group for a finite group G satisfying that G/[G, G] is not a 2-group, where [G, G] is the commutator subgroup of G.

Original languageEnglish
Pages (from-to)91-106
Number of pages16
JournalJournal of the Mathematical Society of Japan
Volume64
Issue number1
DOIs
Publication statusPublished - Oct 5 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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