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CSA-groups and separated free constructions

Published online by Cambridge University Press:  17 April 2009

D. Gildenhuys ,
O. Kharlampovich  and
A. Myasnikov
D. Gildenhuys
Affiliation:
Department of Mathematics and StatisticsMcGill UniversityMontreal QCCanadaH3A 2K6
O. Kharlampovich
Affiliation:
Department of Mathematics and StatisticsMcGill UniversityMontreal QCCanadaH3A 2K6
A. Myasnikov
Affiliation:
Department of Mathematics and StatisticsMcGill UniversityMontreal QCCanadaH3A 2K6
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Abstract

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A group G is called a CSA-group if all its maximal Abelian subgroups are malnormal; that is, Mx ∩ M = 1 for every maximal Abelian subgroup M and x ∈ G − M. The class of CSA-groups contains all torsion-free hyperbolic groups and all groups freely acting on λ-trees. We describe conditions under which HNN-extensions and amalgamated products of CSA-groups are again CSA. One-relator CSA-groups are characterised as follows: a torsion-free one-relator group is CSA if and only if it does not contain F2 × Z or one of the nonabelian metabelian Baumslag-Solitar groups B1, n = 〈x, y | yxy−1 = xn〉, n ∈ Z ∂ {0, 1}; a one-relator group with torsion is CSA if and only if it does not contain the infinite dihedral group.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 1 , August 1995 , pp. 63 - 84
Copyright
Copyright © Australian Mathematical Society 1995

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