Monogenic free inverse semigroups and partial automorphisms of regular rooted trees

E. Kochubinska; A. Oliynyk

doi:10.30970/ms.61.1.3-9

E. Kochubinska Taras Shevchenko National University Kyiv Ukraine
A. Oliynyk Taras Shevchenko National University Kyiv Ukraine https://orcid.org/0000-0003-0940-7731

DOI: https://doi.org/10.30970/ms.61.1.3-9

Keywords: free inverse semigroup;, rooted tree; partial automorphism

Abstract

For a one-to-one partial mapping on an infinite set, we present a criterion in terms of its cycle-chain decomposition that the inverse subsemigroup generated by this mapping is monogenic free inverse.

We also give a sufficient condition for a regular rooted tree partial automorphism to extend to a partial automorphism of another regular rooted tree so that the inverse semigroup gene\-ra\-ted by this extended partial automorphism is monogenic free inverse. The extension procedure we develop is then applied to $n$-ary adding machines.

Author Biographies

E. Kochubinska, Taras Shevchenko National University Kyiv Ukraine

Taras Shevchenko National University

Kyiv Ukraine

A. Oliynyk, Taras Shevchenko National University Kyiv Ukraine

Taras Shevchenko National University

Kyiv Ukraine

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