A necessary condition for the Smith equivalence of G-modules and its sufficiency

Masaharu Morimoto

doi:10.1515/ms-2015-0197

A necessary condition for the Smith equivalence of G-modules and its sufficiency

Masaharu Morimoto

Research output: Contribution to journal › Article › peer-review

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Abstract

Let G be a finite group. In this paper we give a new necessary condition for two real G-modules to be Smith equivalent if G has a normal Sylow 2-subgroup. We show that the condition is also sufficient under certain hypotheses. By results on the Smith equivalence obtained in this paper, the primary Smith sets are not subgroups of the real representation rings for various Oliver groups with normal Sylow 2-subgroups.

Original language	English
Pages (from-to)	979-998
Number of pages	20
Journal	Mathematica Slovaca
Volume	66
Issue number	4
DOIs	https://doi.org/10.1515/ms-2015-0197
Publication status	Published - Aug 1 2016

Keywords

Smith equivalence
Smith set
fixed point
representation

ASJC Scopus subject areas

Mathematics(all)

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10.1515/ms-2015-0197

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AB - Let G be a finite group. In this paper we give a new necessary condition for two real G-modules to be Smith equivalent if G has a normal Sylow 2-subgroup. We show that the condition is also sufficient under certain hypotheses. By results on the Smith equivalence obtained in this paper, the primary Smith sets are not subgroups of the real representation rings for various Oliver groups with normal Sylow 2-subgroups.

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KW - Smith set

KW - fixed point

KW - representation

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A necessary condition for the Smith equivalence of G-modules and its sufficiency

Abstract

Keywords

ASJC Scopus subject areas

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