ON AUTOMORPHISM GROUPS OF ENDOMORPHISM SEMIGROUPS OF FINITE ELEMENTARY ABELIAN GROUPS

Author(s)

ON AUTOMORPHISM GROUPS OF ENDOMORPHISM SEMIGROUPS OF FINITE ELEMENTARY ABELIAN GROUPS Arman Bayramyan

In this article, we explore the automorphisms of endomorphism semigroups and automorphism groups
of the finite elementary Abelian groups. In particular, we prove that
Aut(End(Zp⊕Zp⊕⋯⊕Zp)) can be canonically embedded into
Aut(Aut(Zp⊕Zp⊕⋯⊕Zp)) using an elementary approach based
on matrix operations. We also show that all automorphisms of End(Zp⊕Zp⊕⋯⊕Zp)
are inner.

DOI: 10.46991/PYSU:A/2022.56.2.049 Physical and Mathematical Sciences, 56(2 (258) 49-57

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Keywords

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

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