On Schur p-Groups of odd order

Grigory Ryabov

doi:10.1142/S0219498817500451

On Schur p-Groups of odd order

Grigory Ryabov

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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 language	English
Article number	1750045
Number of pages	29
Journal	Journal of Algebra and its Applications
Volume	16
Issue number	3
DOIs	https://doi.org/10.1142/S0219498817500451
Publication status	Published - 1 Mar 2017

Keywords

Cayley schemes
Permutation groups
S -rings
Schur groups
Srings

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10.1142/S0219498817500451

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