A major result of D.B. McAlister for inverse semigroups is generalised in the paper to classes of regular semigroups, including the class of all regular semigroups. It is shown that any regular semigroup is a homomorphic image of a regular semigroup whose least full self-conjugate subsemigroup is unitary; the homomorphism is injective on the subsemigroup. As an application, the group complexity of any finite E-solid regular semigroup is shown to be the same as, or one more than that of its least full self-conjugate subsemigroup (the subsemigroup is completely regular and is the type II subsemigroup). In an addition to the paper, by P.R. Jones, it is shown that any finite locally orthodox semigroup has group complexity 0 or 1. © 1995.

Item Type:	Refereed Article
Research Division:	Mathematical Sciences
Research Group:	Pure Mathematics
Research Field:	Algebra and Number Theory
Objective Division:	Expanding Knowledge
Objective Group:	Expanding Knowledge
Objective Field:	Expanding Knowledge in the Mathematical Sciences
UTAS Author:	Trotter, PG (Dr Peter Trotter)
ID Code:	6095
Year Published:	1995
Web of Science® Times Cited:	5
Deposited By:	Mathematics
Deposited On:	1995-08-01
Last Modified:	2011-08-25
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