GAP MODULES FOR SEMIDIRECT PRODUCT GROUPS

• SUMI Toshio

  Department of Art and Information Design Faculty of Design Kyushu University

Abstract

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 V^P > 2 dim V^H 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.

Journal

• Kyushu Journal of Mathematics

  Kyushu Journal of Mathematics 58 (1), 33-58, 2004

  Faculty of Mathematics, Kyushu University

Keywords

• General Mathematics

Details

• CRID: 1390001205229034752
• NII Article ID: 130000063078
• NII Book ID: AA10994346
• DOI: 10.2206/kyushujm.58.33
• ISSN: 18832032
• ISSN: 13406116
• MRID: 2053718
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/58/1/58_1_33/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed