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Mathematica Slovaca

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Volume 66, Issue 4


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

Masaharu Morimoto
  • Department of Mathematics Graduate School of Natural Science and Technology Okayama University 3-1-1 Tsushimanaka, Kitaku Okayama, 700-8530 Japan
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Published Online: 2016-11-03 | DOI: https://doi.org/10.1515/ms-2015-0197


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.

MSC 2010: Primary 57S17; Secondary 20C15

keywords: Smith equivalence; Smith set; fixed point; representation


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About the article

Received: 2013-12-03

Accepted: 2014-03-23

Published Online: 2016-11-03

Published in Print: 2016-08-01

Citation Information: Mathematica Slovaca, Volume 66, Issue 4, Pages 979–998, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0197.

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