Classification of abelian Schur groups II

Fuente: arXiv
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Main Author: Ryabov, Grigory
Format: Preprint
Published: 2026
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author Ryabov, Grigory
author_facet Ryabov, Grigory
contents A finite group $G$ is called a Schur group if every Schur ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of the symmetric group $Sym(G)$ that contains all right translations of $G$. The list of all possible abelian Schur groups was obtained by Evdokimov, Kovács, and Ponomarenko in 2016. In two papers, we complete a classification of abelian Schur groups. In the present paper, we prove that several groups of nonpowerful order from the list are Schur groups. By that, we obtain a classification of abelian Schur groups.
format Preprint
id arxiv_https___arxiv_org_abs_2605_18356
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Classification of abelian Schur groups II
Ryabov, Grigory
Combinatorics
Group Theory
05E30, 20B25
A finite group $G$ is called a Schur group if every Schur ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of the symmetric group $Sym(G)$ that contains all right translations of $G$. The list of all possible abelian Schur groups was obtained by Evdokimov, Kovács, and Ponomarenko in 2016. In two papers, we complete a classification of abelian Schur groups. In the present paper, we prove that several groups of nonpowerful order from the list are Schur groups. By that, we obtain a classification of abelian Schur groups.
title Classification of abelian Schur groups II
topic Combinatorics
Group Theory
05E30, 20B25
url https://arxiv.org/abs/2605.18356