Journal of the Mathematical Society of Japan

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

Toshio SUMI

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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) VL = 0 for any normal subgroup L of G with prime power index. (2) dim VP > 2 dim VH for any P < HG 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.

Article information

J. Math. Soc. Japan, Volume 64, Number 1 (2012), 91-106.

First available in Project Euclid: 26 January 2012

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Zentralblatt MATH identifier

Primary: 57S17: Finite transformation groups
Secondary: 20C15: Ordinary representations and characters

gap group gap module representation


SUMI, Toshio. The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2. J. Math. Soc. Japan 64 (2012), no. 1, 91--106. doi:10.2969/jmsj/06410091.

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