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Varieties of groups and of completely simple semigroups

Published online by Cambridge University Press:  17 April 2009

Mario Petrich  and
Norman R. Reilly
Mario Petrich
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada.
Norman R. Reilly
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada.
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Abstract

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Completely simple semigroups form a variety if we consider them both with the multiplication and the operation of inversion. Denote the lattice of all varieties of completely simple semi-groups by L(CS) and that of varieties of groups by L(G). We prove that the mappings V → V ∩ G and V → V v G are homomorphisms of L(CS) onto L(G) and the interval [G, CS], respectively. The homomorphism V → (V ∩ G, V v G) is an isomorphism of L(CS) onto a subdirect product. We explore different properties of the congruences on L(CS) induced by these homomorphisms.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 3 , June 1981 , pp. 339 - 359
Copyright
Copyright © Australian Mathematical Society 1981

References

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