Endomorphisms and partial isomorphisms

Peter J. Cameron

doi:10.1007/s00233-025-10514-5

Endomorphisms and partial isomorphisms

Peter J. Cameron^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Let A be an algebra (in the sense of universal algebra). Define PISo(A) to be the inverse semigroup of partial isomorphisms of A, and End(A) the semigroup of endomorphisms of A. The purpose of this note is to record the following result.

Theorem 1
Let A be a finite abelian group. Then |PIso(A)| = |End(A)|.

Original language	English
Number of pages	2
Journal	Semigroup Forum
Volume	Online first
Early online date	14 Mar 2025
DOIs	https://doi.org/10.1007/s00233-025-10514-5
Publication status	E-pub ahead of print - 14 Mar 2025

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title = "Endomorphisms and partial isomorphisms",

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AB - Let A be an algebra (in the sense of universal algebra). Define PISo(A) to be the inverse semigroup of partial isomorphisms of A, and End(A) the semigroup of endomorphisms of A. The purpose of this note is to record the following result.Theorem 1 Let A be a finite abelian group. Then |PIso(A)| = |End(A)|.

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M3 - Article

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Endomorphisms and partial isomorphisms

Abstract

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