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A group variety defined by a semigroup law

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

A. Yu. Ol'shanskii  and
A. Storozhev
A. Yu. Ol'shanskii
Affiliation:
Department of MathematicsMoscow State UniversityLeninskie Gory, Moscow, 119899Russia e-mail: [email protected]
A. Storozhev
Affiliation:
Australian Mathematics TrustUnivesity of CanberraPO Box 1, Belconnen, ACT 2616Australia e-mail: [email protected]
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Abstract

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A group variety defined by one semigroup law in two variables is constructed and it is proved that its free group is not a periodic extension of a locally soluble group.

MSC classification

Secondary: 20E10: Quasivarieties and varieties of groups 20F06: Cancellation theory; application of van Kampen diagrams
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 2 , April 1996 , pp. 255 - 259
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Lewin, J. A. and Lewin, T., ‘Semigroup laws in varieties of solvable groups’, Proc. Cambridge Philos. Soc. 65 (1969), 1–9.CrossRefGoogle Scholar
[2]Longobardi, P., Maj, M. and Rhemtulla, A. H., ‘Groups with no free subsemigroups’, Proc. Amer. Math. Soc., to appear.Google Scholar
[3]Ol'shanskii, A. Yu., Geometry of definig relations in groups, Mathematics and its applications volume 70 (Soviet Series) (Kluwer Academic Publishers, Dordrecht, 1991).CrossRefGoogle Scholar
[4]Shirshov, A. I., ‘On some positively defined group varieties’, Sib. Mat. J. 8 (1967), 1190–1192.Google Scholar
[5]Storozhev, A., ‘On abelian subgroups of relatively free groups’, Comm. Algebra 22 (1994), 2677–2701.CrossRefGoogle Scholar