Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2025-01-03T17:53:22.560Z Has data issue: false hasContentIssue false
  • English
  • Français

Soluble and linear repetitive groups

Published online by Cambridge University Press:  17 April 2009

A.V. Kelarev  and
P.V. Shumyatsky
A.V. Kelarev
Affiliation:
Department of Mathematics, The University of Tasmania, Hobart, Tas 7001, Australia
P.V. Shumyatsky
Affiliation:
Department of Mathematics, Technion - Israel Institute of Technology, 32000 Haifa, Israel
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.

Our main theorem describes FC-soluble and linear repetitive groups. As a corollary, we characterise algebraic linear repetitive semigroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 253 - 261
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Adjan, S.I., The Burnside problem and identities in groups (Springer-Verlag, Berlin, Heidelberg, New York, 1978).Google Scholar
[2]Blyth, R.D. and Rhemtulla, A.H., ‘Rewritable products in FC-by-finite groups’, Canad. J. Math. 41 (1989), 369–384.CrossRefGoogle Scholar
[3]Howie, J.M., An introduction to semigroup theory (Academic Press, New York, 1976).Google Scholar
[4]Justin, J., ‘Groupes et semi-groupes à croissance linéaire’, C. R. Acad. Sci. Paris 273 (1971), 212–214.Google Scholar
[5]Justin, J., ‘Sur une construction de Bruck et Reilly’, Semigroup Forum 3 (1971), 148–155.CrossRefGoogle Scholar
[6]Justin, J., ‘Généralisation du théoremè de van der Waerden sur les semi-groupes rèpètitifs’, J. Combin. Theory Ser. A. 12 (1972), 357–367.CrossRefGoogle Scholar
[7]Justin, J., ‘Characterization of the repetitive commutative semigroups’, J. Algebra 21 (1972), 87–90.CrossRefGoogle Scholar
[8]Justin, J., ‘Groupes linéaires rép´etitifs’, C.R. Acad. Sci. Paris 292 (1981), 349–350.Google Scholar
[9]Justin, J. and Pirillo, G., ‘Une condition de finitude pour les semi-groupes finiment en-gendrés’, C.R. Acad. Sci. Paris 306 (1988), 63–65.Google Scholar
[10]Justin, J. and Pirillo, G., ‘Factorial languages and some combinatorial properties of semigroups’, Internat. J. Algebra Comput. 3 (1993), 295–316.CrossRefGoogle Scholar
[11]Justin, J. and Pirillo, G., ‘On some questions and conjectures in combinatorial semigroup theory Southeast Asian Bull. Math.’ 18, pp. 91–104.Google Scholar
[12]Justin, J., Pirillo, G. and Varricchio, S., ‘Unavoidable regularities and finiteness conditions for semigroups’, in Theoretical Computer Science, (Bertoni, , Böhm, and Migliolo, , Editors), Proceedings of the Third Italian Conference Mantova, 2–4 November 1989 (World Scientific, 1989).Google Scholar
[13]Kelarev, A.V., ‘Combinatorial properties and homomorphisms of semigroups’, Internat. J. Algebra Comput. (to appear).Google Scholar
[14]Krause, G.R. and Lenagan, T.H., Growth of algebras and Gelfand-Kirillov dimension, Research Notes 116 (Pitman, Boston, 1985).Google Scholar
[15]Lothaire, M., Combinatorics on words (Addison-Wesley, London, 1983).Google Scholar
[16]Pirillo, G., ‘On a finiteness condition for a finitely generated semigroup’, Rend. Circ. Math. Palermo 2 38 (1989), 212–216.CrossRefGoogle Scholar
[17]Putcha, M.S., Linear algebraic monoids, London Math. Soc. Lect. Notes Ser. 133 (Cambridge University Press, Cambridge, 1988).CrossRefGoogle Scholar
[18]Robinson, D.J.S., A course in the theory of groups (Springer-Verlag, Berlin, Heidelberg, New York, (1982)).CrossRefGoogle Scholar
[19]Tits, J., ‘Free subgroups in linear groups’, J. Algebra 20 (1972), 250–270.CrossRefGoogle Scholar
[20]Tomkinson, M.J., FC-groups (Pitman, London, 1984).Google Scholar
[21]Wehrfritz, B.A.F., Infinite linear groups (Springer-Verlag, Berlin, Heidelberg, New York, 1973).CrossRefGoogle Scholar