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This article is cited in 3 scientific papers (total in 3 papers)
The Schur–Wielandt theory for central $S$-rings
M. E. Muzychuka, I. N. Ponomarenkob, G. Chenc a Netanya Academic College, Netanya, Israel
b St. Petersburg Branch of Steklov Institute of Mathematics, St. ;Petersburg, Russia
c School of Mathematics and Statistics, Central China Normal University, Wuhan, China
Abstract:
Two basic results on $S$-rings over an Abelian group are the Schur theorem on multipliers and the Wielandt theorem on primitive $S$-rings over groups with a cyclic Sylow subgroup. Neither of these is directly generalized to the non-Abelian case. Nevertheless, we prove that the two theorems are true for central $S$-rings over any group, i.e., for $S$-rings that are contained in the center of the group ring of that group (such $S$-rings arise naturally in the supercharacter theory). Extending the concept of a $B$-group introduced by Wielandt, we show that every Camina group is a generalized $B$-group, whereas simple groups, with few exceptions, cannot be of this type.
Keywords:
$S$-ring, conjugacy class, $B$-group.
Received: 24.05.2015
Citation:
M. E. Muzychuk, I. N. Ponomarenko, G. Chen, “The Schur–Wielandt theory for central $S$-rings”, Algebra Logika, 55:1 (2016), 58–74; Algebra and Logic, 55:1 (2016), 38–49
Linking options:
https://www.mathnet.ru/eng/al729 https://www.mathnet.ru/eng/al/v55/i1/p58
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Abstract page: | 168 | Full-text PDF : | 42 | References: | 29 | First page: | 8 |
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