On Schur p-Groups of odd order

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Abstract

A finite group G is called a Schur group if any S-ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. We prove that the groups Z3 × Z3n, where n ≥ 1, are Schur. Modulo previously obtained results, it follows that every noncyclic Schur p-group, where p is an odd prime, is isomorphic to Z3 × Z3 × Z3 or Z3 × Z3n, n ≥ 1.

Original languageEnglish
Article number1750045
Number of pages29
JournalJournal of Algebra and its Applications
Volume16
Issue number3
DOIs
Publication statusPublished - 1 Mar 2017

Keywords

  • Cayley schemes
  • Permutation groups
  • S -rings
  • Schur groups
  • Srings

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