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

Let be a finite group. In this paper we give a new necessary condition for two real -modules to be Smith equivalent if 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...

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Bibliographic Details
Published inMathematica Slovaca Vol. 66; no. 4; pp. 979 - 998
Main Author Morimoto, Masaharu
Format Journal Article
LanguageEnglish
Published Heidelberg De Gruyter 01.08.2016
Walter de Gruyter GmbH
Subjects
Equivalence
fixed point
Hypotheses
Mathematical analysis
Primary 57S17
representation
Representations
Secondary 20C15
Smith equivalence
Smith set
Subgroups
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Summary:Let be a finite group. In this paper we give a new necessary condition for two real -modules to be Smith equivalent if 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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0139-9918
1337-2211
DOI:10.1515/ms-2015-0197