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Semilattices with a transitive automorphism group

Part of: Ordered sets Semigroups

Published online by Cambridge University Press:  09 April 2009

F. Pastijn
F. Pastijn
Affiliation:
University of Nebraska-LincolnLincoln, NE 68588, U.S.A. Rijksuniversiteit Gent B-9000 Gent Belgium
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Abstract

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If L is any semilattice, let TL denote the Munn semigroup of L, and Aut (L) the automorphism group of L.

We show that every semilattice L can be isomorphically embedded as a convex subsemilattice in a semilattice L' which has a transitive automorphism group in such a way that (i) every partial isomorphism α of L can be extended to an automorphism of L', (ii) every partial isomorphism: α: eL → fL of L can be extended to a partial isomorphism αL′: eL′ → fL′ of L′ such that TL → TL′, α → αL′ embeds TL' isomorphically in TL′, (iii) every automorphism γ of L can be extended to an automorphism γL′ of L′ such that Aut (L) → Aut (L′), γ → γL embeds Aut (L) isomorphically in Aut (L′).

MSC classification

Secondary: 06A12: Semilattices 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 1 , February 1980 , pp. 29 - 34
Copyright
Copyright © Australian Mathematical Society 1980

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