ON AUTOMORPHISM GROUPS OF ENDOMORPHISM SEMIGROUPS OF FINITE ELEMENTARY ABELIAN GROUPS
DOI:
https://doi.org/10.46991/PYSU:A/2022.56.2.049Keywords:
automorphisms of matrix semigroups, finite elementary Abelian groups, automorphisms of endomorphism semigroupAbstract
In this article, we explore the automorphisms of endomorphism semigroups and automorphism groupsof 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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