Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-18T05:00:47.108Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

[1]Bennett, P., ‘On the structure of inverse semigroup amalgams’, Int. J. Algebra Comput. (5) 7 (1997), 577–604.CrossRefGoogle Scholar
[2]Cherubini, A., Meakin, J. C. and Piochi, B., ‘Amalgams of free inverse semigroups’, Semigroup Forum 54 (1997), 199–220.CrossRefGoogle Scholar
[3]Cohen, D. E., Combinatorial group theory: A topological approach (Cambridge University Press, Cambridge, 1989).CrossRefGoogle Scholar
[4]Haataja, S., Margolis, S. W. and Meakin, J. C., ‘On the structure of full regular semigroup amalgams’, J. Algebra 183 (1996), 38–54.CrossRefGoogle Scholar
[5]Hall, T. E., ‘Free products with amalgamation of inverse semigroups’, J. Algebra 34 (1975), 375–385.CrossRefGoogle Scholar
[6]Hall, T. E., ‘Amalgamation of inverse and regular semigroups’, Trans. Amer. Math. Soc. 246 (1978), 395–406.CrossRefGoogle Scholar
[7]Howie, J. M., ‘Embedding theorems for semigroups’, Quart. J. Math. 14 (1963), 254–258.CrossRefGoogle Scholar
[8]Jajcayova, T., HNN extensions of inverse semigroups (Ph.D. Thesis, University of Nebraska-Lincoln, 1997).Google Scholar
[9]Lawson, M. V., Inverse semigroups (World Scientific, Singapore, 1998).CrossRefGoogle Scholar
[10]Lyndon, R. C. and Schupp, P. E., Combinatorial group theory (Springer, New York, 1976).Google Scholar
[11]Margolis, S. W. and Meakin, J. C., ‘Inverse monoids, trees and context-free languages’, Trans. Amer. Math. Soc. 335 (1993), 259–276.Google Scholar
[12]Meakin, J. C. and Yamamura, A., ‘Bass-Serre theory and inverse monoids’, in: Semigroups and Applications (eds. Howie, J. M. and Ruškuc, N.) (World Scientific, Singapore, 1998) pp. 125–140.Google Scholar
[13]Petrich, M., Inverse semigroups (Wiley, New York, 1984).Google Scholar
[14]Serre, J.-P., Trees (Springer, New York, 1980).CrossRefGoogle Scholar
[15]Yamamura, A., HNN extensions of inverse semigroups (Ph.D. Thesis, University of Nebraska-Lincoln, 1996).Google Scholar
[16]Yamamura, A., ‘HNN extensions of inverse semigroups and applications’, Int. J. Algebra Comput. (5) 7 (1997), 605–624.CrossRefGoogle Scholar
[17]Yamamura, A., ‘HNN extensions of semilattices’, Int. J. Algebra Comput. (5) 9 (1999), 555–596.CrossRefGoogle Scholar
[18]Yamamura, A., ‘Presentations of Bruck-Reilly extensions and decision problems’, Semigroup Forum (to appear).Google Scholar