ON AUTOMORPHISM GROUPS OF ENDOMORPHISM SEMIGROUPS OF FINITE ELEMENTARY ABELIAN GROUPS

Arman A. Bayramyan

doi:10.46991/PYSU:A/2022.56.2.049

Authors

Arman A. Bayramyan Chair of Algebra and Geometry, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2022.56.2.049

Keywords:

automorphisms of matrix semigroups, finite elementary Abelian groups, automorphisms of endomorphism semigroup

Abstract

In this article, we explore the automorphisms of endomorphism semigroups and automorphism groups
of the finite elementary Abelian groups. In particular, we prove that
$\mathrm{Aut}(\mathrm{End}(\Z_p\oplus\Z_p\oplus\cdots\oplus\Z_p))$ can be canonically embedded into
$\mathrm{Aut}(\mathrm{Aut}(\Z_p\oplus\Z_p\oplus\cdots\oplus\Z_p))$ using an elementary approach based
on matrix operations. We also show that all automorphisms of $\mathrm{End}(\Z_p\oplus\Z_p\oplus\cdots\oplus\Z_p)$
are inner.

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