On the group of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\)

O. Gutik, I. Pozdniakova

Abstract


We study automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\) and prove that the group \(\mathbf{Aut}(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}})\) of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) is isomorphic to the additive group of integers.

Keywords


bicyclic monoid, inverse semigroup, bicyclic extension, automorphism, group of automorphism, order-convex set, order isomorphism

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DOI: http://dx.doi.org/10.12958/adm2010

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