ON AUTOMORPHISM GROUPS OF ENDOMORPHISM SEMIGROUPS OF FINITE ELEMENTARY ABELIAN GROUPS

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.