Natural Science, Mathematics, 2025
ON AUTOMORPHISM GROUPS OF ENDOMORPHISM SEMIGROUPS OF FINITE ELEMENTARY ABELIAN GROUPS
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Submitted: 2025-01-22; Published: 2025-01-22
Ā© 2025 by author(s) and The Gufo Inc.
This work is licensed under Creative Commons AttributionāNonCommercial International License
(CC BY-NC 4.0).
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
Aut(End(ZpāZpāāÆāZp))Ā can be canonically embedded into
Aut(Aut(ZpāZpāāÆāZp))Ā using an elementary approach based
on matrix operations. We also show that all automorphisms ofĀ End(ZpāZpāāÆāZp)
are inner.