TY - JOUR

T1 - On Schur p-Groups of odd order

AU - Ryabov, Grigory

N1 - Publisher Copyright: © 2017 World Scientific Publishing Company.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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.

AB - 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.

KW - Cayley schemes

KW - Permutation groups

KW - S -rings

KW - Schur groups

KW - Srings

UR - http://www.scopus.com/inward/record.url?scp=84962719367&partnerID=8YFLogxK

U2 - 10.1142/S0219498817500451

DO - 10.1142/S0219498817500451

M3 - Article

AN - SCOPUS:84962719367

VL - 16

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

SN - 0219-4988

IS - 3

M1 - 1750045

ER -