2008年
The Smith sets of finite groups with normal Sylow 2-subgroups and small nilquotients
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY
- ,
- ,
- 巻
- 48
- 号
- 1
- 開始ページ
- 219
- 終了ページ
- 227
- 記述言語
- 英語
- 掲載種別
- 出版者・発行元
- KINOKUNIYA CO LTD
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. Pawalowski-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.
- リンク情報
- ID情報
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- ISSN : 0023-608X
- Web of Science ID : WOS:000257766800010