TY - JOUR

T1 - Gap modules for semidirect product groups

AU - Sumi, Toshio

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2004

Y1 - 2004

N2 - Let G be a finite group not of prime power order. A gap G-module V is a finite-dimensional real G-representation space satisfying the following two conditions. The first is the condition dim Vp >2dim VH for all P<H ≤ G such that P is of prime power order and the other is the condition that V has only one H-fixed point 0 for all large subgroups H: precisely to say, H ? L(G). If there exists a gap G-module, then G is called a gap group. We study G-modules induced from C-modules for subgroups C of G and obtain a sufficient condition for G to become a gap group. Consequently, we show that non-solvable general linear groups and the automorphism groups of sporadic groups are all gap groups.

AB - Let G be a finite group not of prime power order. A gap G-module V is a finite-dimensional real G-representation space satisfying the following two conditions. The first is the condition dim Vp >2dim VH for all P<H ≤ G such that P is of prime power order and the other is the condition that V has only one H-fixed point 0 for all large subgroups H: precisely to say, H ? L(G). If there exists a gap G-module, then G is called a gap group. We study G-modules induced from C-modules for subgroups C of G and obtain a sufficient condition for G to become a gap group. Consequently, we show that non-solvable general linear groups and the automorphism groups of sporadic groups are all gap groups.

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U2 - 10.2206/kyushujm.58.33

DO - 10.2206/kyushujm.58.33

M3 - Article

AN - SCOPUS:84866917301

SN - 1340-6116

VL - 58

SP - 33

EP - 58

JO - Kyushu Journal of Mathematics

JF - Kyushu Journal of Mathematics

IS - 1

ER -