This article is cited in 1 paper

MATHEMATICS

Determinability of a completely decomposable rank 3 group by its automorphism group

E. A. Timoshenko, I. V. Tretyakov

Tomsk State University, Tomsk, Russian Federation

Abstract: In the work of Vildanov, Gaidak, and Timoshenko, all completely decomposable groups of rank 2 were found that are defined by their automorphism group in the class of all completely decomposable groups. In this article, a similar problem is solved for groups of rank 3. It is shown that a completely decomposable group of rank 3 is determined by its automorphism group if and only if it is a direct sum of three almost divisible summands of rank 1, two of which are isomorphic to each other and embed into the third.

Keywords: matrix, involution, completely decomposable group, automorphism group.

UDC: 512.54

MSC: 15B33, 20H25, 20K15

Received: 20.12.2021
Accepted: March 22, 2022

DOI: 10.17223/19988621/76/3

Bibliographic databases:

•