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ON FREE SPECTRA OF A CLASS OF FINITE INVERSE MONOIDS

Part of: Varieties Semigroups

Published online by Cambridge University Press:  07 March 2013

IGOR DOLINKA
IGOR DOLINKA*
Affiliation:
Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21101 Novi Sad, Serbia email [email protected]
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Abstract

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For a finite Clifford inverse algebra $A$, with natural order meet-semilattice ${Y}_{A} $ and group of units ${G}_{A} $, we show that the inverse monoid obtained as the semidirect product ${ Y}_{A}^{1} {\mathop{\ast }\nolimits}_{\rho } {G}_{A} $ has a log-polynomial free spectrum whenever $\rho $ is a term-expressible left action of ${G}_{A} $ on ${Y}_{A} $ and all subgroups of $A$ are nilpotent. This yields a number of examples of finite inverse monoids satisfying the Seif conjecture on finite monoids whose free spectra are not doubly exponential.

Keywords

free spectrumfinite inverse monoidsemidirect productClifford inverse algebra

MSC classification

Secondary: 20M05: Free semigroups, generators and relations, word problems 20M18: Inverse semigroups 08B20: Free algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 93 , Issue 3 , December 2012 , pp. 225 - 237
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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