The Schur–Wielandt Theory for Central S-Rings

M. E. Muzychuk, I. N. Ponomarenko, G. Chen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)38-49
Number of pages12
JournalAlgebra and Logic
Volume55
Issue number1
DOIs
StatePublished - 1 Mar 2016
Externally publishedYes

Keywords

  • B-group
  • S-ring
  • conjugacy class

ASJC Scopus subject areas

  • Analysis
  • Logic

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