Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-15T05:50:26.687Z Has data issue: false hasContentIssue false

Relative Abelian kernels of some classes of transformation monoids

Published online by Cambridge University Press:  17 April 2009

E. Cordeiro
Affiliation:
Instituto Politécnico de Bragança, Escola Superior de Tecnologia e Gestão, Campus de Santa Apolónia, 5301-857 Bragança, Portugal, e-mail: emc@ipb.pt
M. Delgado
Affiliation:
Departamento de Matemática Pura, Faculdade de Ciências, 4169-007 Porto, Portugal, e-mail: quadmdelgado@fc.up.pt
V.H. Fernandes
Affiliation:
Departamento de Matemática, Universidade Nova de Lisboa, Monte da Caparica, 2829-516 Caparica, Portugal, C.A.U.L., 1649-003 Lisboa, Portugal, e-mail: vhf@fct.unl.pt
Rights & Permissions [Opens in a new window]

Extract

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 consider the symmetric inverse monoid ℐn of an n-element chain and its inverse submonoids ℐn, ℐn, ℐn and ℘ℐn of all order-preserving, order-preserving or order-reversing, orientation-preserving and orientation-preserving or orientation-reversing transformations, respectively, and give descriptions of their Abelian kernels relative to decidable pseudovarieties of Abelian groups.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Almeida, J., Finite semigroups and universal algebra, (English translation) (World Scientific, Singapore, 1995).CrossRefGoogle Scholar
[2]Almeida, J. and Steinberg, B., ‘Iterated semidirect products with applications to complexity’, Proc. London Math. Soc. 80 (2000), 5074.Google Scholar
[3]Ash, C.J., ‘Inevitable graphs: a proof of the type II conjecture and some related decision procedures’, Internet. J. Algebra Comput. 1 (991), 127146.CrossRefGoogle Scholar
[4]Cordeiro, E. and Delgado, M., ‘Computing relative abelian kernels of finite monoids’, J. of Algebra (to appear).Google Scholar
[5]Delgado, M., ‘Abelian pointlikes of a monoid’, Semigroup Forum 56 (1998), 339361.Google Scholar
[6]Delgado, M., ‘Commutative images of rational languages and the abelian kernel of a monoid’, Theor. Inform. Appl. 35 (2001), 419435.CrossRefGoogle Scholar
[7]Delgado, M. and Fernandes, V.H., ‘Abelian kernels of some monoids of injective partial transformations and an application’, Semigroup Forum 61 (2000), 435452.CrossRefGoogle Scholar
[8]Delgado, M. and Fernandes, V.H., ‘Solvable monoids with commuting idempotents’, Internat. J. Algebra Comput. 15 (2005), 547570.CrossRefGoogle Scholar
[9]Delgado, M. and Fernandes, V.H., ‘Abelian kernels of monoids of order-preserving maps and of some of its extensions’, Semigroup Forum 68 (2004), 435456.CrossRefGoogle Scholar
[10]Delgado, M., Fernandes, V.H., Margolis, S. and Steinberg, B., ‘On semigroups whose idempotent-generated subsemigroup is aperiodic’, Internat. J. Algebra Comput. 14 (2004), 655665.CrossRefGoogle Scholar
[11]Delgado, M. and Morais, J., ‘SgpViz, a GAP [27] package to visualize finite semigroups (http://www.gap-system.org/Packages/sgpviz.html)’.Google Scholar
[12]Dummit, M.S. and Foote, R.M., Abstract algebra (Prentice-Hall, Englewood Cliffs, 1991).Google Scholar
[13]Fernandes, V.H., ‘Semigroups of order-preserving mappings on a finite chain: a new class of divisors’, Semigroup Forum 54 (1997), 230236.CrossRefGoogle Scholar
[14]Fernandes, V.H., ‘The monoid of all injective orientation-preserving partial transformations on a finite chain’, Comm. Algebra 28 (2000), 34013426.CrossRefGoogle Scholar
[15]Fernandes, V.H., ‘The monoid of all injective order-preserving partial transformations on a finite chain’, Semigroup Forum 62 (2001), 178204.Google Scholar
[16]Fernandes, V.H., ‘Presentations for some monoids of partial transformations on a finite chain: a survey’, in Semigroups, Algorithms, Automata and Languages, (Gomes, G.M.S., Pin, J.-E. and Silva, P.V., Editors) (World Scientific, River Edge, N.J., 2002), pp. 363378.CrossRefGoogle Scholar
[17]Fernandes, V.H., Gomes, G.M.S. and Jesus, M.M., ‘Presentations for some monoids of injective partial transformations on a finite chain’, Southeast Asian Bull. Math. 28 (2004), 903918.Google Scholar
[18]Henckell, K., Margolis, S., Pin, J.-E. and Rhodes, J., ‘Ash's type II theorem, profinite topology and Malcev products. Part I’, Internat. J. Algebra Comput. 1 (1991), 411436.Google Scholar
[19]Herwig, B. and Lascar, D., ‘Extending partial automorphisms and the profinite topology on free groups’, Trans. Amer. Math. Soc. 352 (2000), 19852021.CrossRefGoogle Scholar
[20]Howie, J.M., Fundamentals of semigroup theory, London Mathematical Society Monographs. New Series 12 (Oxford University Press, New York, 1995).Google Scholar
[21]Moore, E.H., ‘Concerning the abstract groups of order k! and ½k! holohedrically isomorphic with the symmetric and the alternating substitution groups on k letters’, Proc. London Math. Soc. (1) 28 (1897), 357366.Google Scholar
[22]Popova, L.M., ‘The defining relations of certain semigroups of partial transformations of a finite set’, (Russian), Leningradskij gosudarstvennyj pedagogicheskij institut imeni A. I. Gerzena, Uchenye Zapiski 218 (1961), 191212.Google Scholar
[23]Rhodes, J. and Tilson, B., ‘Improved lower bounds for the complexity of finite semigroups’, J. Pure Appl. Algebra 2 (1972), 1371.CrossRefGoogle Scholar
[24]Ribes, L. and Zalesskiĭ, P.A., ‘On the profinite topology on a free group’, Bull. London Math. Soc. 25 (1993), 3743.CrossRefGoogle Scholar
[25]Ribes, L. and Zalesskiĭ, P.A., ‘The pro-p topology of a free group and algorithmic problems in semigroups’, Internat. J. Algebra Comput. 4 (1994), 359374.Google Scholar
[26]Steinberg, B., ‘Monoid kernels and profinite topologies on the free Abelian group’, Bull. Austral. Math. Soc. 60 (1999), 391402.CrossRefGoogle Scholar
[27]The GAP Group., ‘GAP - groups, algorithms, and programming, Version 4.4’, (2004). (http://www.gap-system.org).Google Scholar