MATHEMATICS

Involutions of the automorphism group of a completely decomposable finite-rank Abelian group

E. A. Timoshenko, I. V. Tretyakov

Tomsk State University, Tomsk, Russian Federation

Abstract: In the framework of the study of questions of the definability of a completely decomposable Abelian group of finite rank by its group of automorphisms, it is shown that any set of pairwise permutable involutions of such a group of automorphisms, which has some additional properties, is conjugate with a set of diagonal involutions.

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

UDC: 512.54

MSC: 15B33, 20H25, 20K15

Received: 02.09.2022
Accepted: December 4, 2023

DOI: 10.17223/19988621/86/13