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Locally full HNN extensions of inverse semigroups

Part of: Structure and classification of infinite or finite groups Semigroups

Published online by Cambridge University Press:  09 April 2009

Akihiro Yamamura
Akihiro Yamamura
Affiliation:
Communications Research Laboratory 4-2-1, Nukui-Kitamachi, Koganei Tokyo 184-8795Japan e-mail: [email protected]
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Abstract

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We investigate a locally full HNN extension of an inverse semigroup. A normal form theorem is obtained and applied to the word problem. We construct a tree and show that a maximal subgroup of a locally full HNN extension acts on the tree without inversion. Bass-Serre theory is employed to obtain a group presentation of the maximal subgroup as a fundamental group of a certain graph of groups associated with the D-structure of the original semigroup.

Keywords

HNN extensionsInverse semigroupsNormal formWord problemBass-Serre theory.

MSC classification

Secondary: 20M18: Inverse semigroups 20M05: Free semigroups, generators and relations, word problems 20E08: Groups acting on trees 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 2 , April 2001 , pp. 235 - 272
Copyright
Copyright © Australian Mathematical Society 2001

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