On Schur p-groups of odd order

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 ${\mathbb{Z}}_3\times {\mathbb{Z}}_{3^n}$, where $n\ge 1$, are Schur. Modulo previously obtained results, it follows that every noncyclic Schur $p$-group, where $p$ is an odd prime, is isomorphic to ${\mathbb{Z}}_3\times {\mathbb{Z}}_3\times {\mathbb{Z}}_3$ or ${\mathbb{Z}}_3\times {\mathbb{Z}}_{3^n}$, $n\ge 1$ .

21 pages. arXiv admin note: text overlap with arXiv:1503.02621 by other authors

Cited by in corpus (2)

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