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

  • Masaharu Morimoto EMAIL logo
Published/Copyright: November 3, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 4

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.

MSC 2010: Primary 57S17; Secondary 20C15
keywords: Smith equivalence; Smith set; fixed point; representation

(Communicated by Július Korbaš)

Acknowledgements

The author would like to thank Július Korbaš and the referee for their carefully reading a draft and giving valuable comments.

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Received: 2013-12-3
Accepted: 2014-3-23
Published Online: 2016-11-3
Published in Print: 2016-8-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0197
Keywords for this article
Smith equivalence; Smith set; fixed point; representation

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