The Smith sets of finite groups with normal Sylow 2-subgroups and small nilquotients

Akihiro Koto, Masaharu Morimoto, Yan Qi

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The Smith equivalence of real representations of a finite group has been studied by many mathematicians, e.g. J. Milnor, T. Petrie, S. Cappell-J. Shaneson, K. Pawałowski-R. Solomon. For a given finite group, let the primary Smith set of the group be the subset of real representation ring consisting of all differences of pairs of prime matched, Smith equivalent representations. The primary Smith set was rarely determined for a nonperfect group G besides the case where the primary Smith set is trivial. In this paper we determine the primary Smith set of an arbitrary Oliver group such that a Sylow 2-subgroup is normal and the nilquotient is isomorphic to the direct product of a finite number of cyclic groups of order 2 or 3. In particular, we answer to a problem posed by T. Sumi.

Original languageEnglish
Pages (from-to)219-227
Number of pages9
JournalKyoto Journal of Mathematics
Volume48
Issue number1
Publication statusPublished - 2008

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Finite Group
Subgroup
Direct Product
Cyclic group
Trivial
Isomorphic
Equivalence
Ring
Subset
Arbitrary

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Smith sets of finite groups with normal Sylow 2-subgroups and small nilquotients. / Koto, Akihiro; Morimoto, Masaharu; Qi, Yan.

In: Kyoto Journal of Mathematics, Vol. 48, No. 1, 2008, p. 219-227.

Research output: Contribution to journalArticle

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