TY - JOUR

T1 - The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2

AU - Sumi, Toshio

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

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U2 - 10.2969/jmsj/06410091

DO - 10.2969/jmsj/06410091

M3 - Article

AN - SCOPUS:84866942403

VL - 64

SP - 91

EP - 106

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 1

ER -