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Generators for the bounded automorphisms of infinite-rank free nilpotent groups

Published online by Cambridge University Press:  17 April 2009

R.G. Burns  and
Lian Pi
R.G. Burns
Affiliation:
Department of Mathematics, York University, Downsview, Toronto, Ontario, Canada
Lian Pi
Affiliation:
Department of Mathematics, York University, Downsview, Toronto, Ontario, Canada
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Abstract

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It is shown that the natural generalisations of the elementary Nielsen transformations of a free group to the infinite-rank case, furnish generators for the subgroup of “bounded” automorphisms of any relatively free nilpotent group of infinite rank. This settles the nilpotent analogue of a question of D. Solitar concerning the “bounded” automorphisms of absolutely free groups of infinite rank.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 2 , October 1989 , pp. 175 - 187
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Bryant, R.M. and Macedońska, O., ‘Automorphisms of relatively free nilpotent groups of infinite rank’, J. Algebra (to appear).Google Scholar
[2]Cohen, D.E., ‘Characteristic subgroups of some relatively free groups’, J. London Math. Soc. 43 (1968), 445–451.CrossRefGoogle Scholar
[3]Cohen, J.M., ‘Aspherical 2-complexes’, J. Pure Appl. Algebra 12 (1978), 101–110.Google Scholar
[4]Cohen, R., ‘Classes of automorphisms of free groups of infinite rank’, Trans. Amer. Math. Soc. 177 (1973), 99–120.CrossRefGoogle Scholar
[5]Hall, M. Jr., The Theory of Groups (Macmillan, New York, 1959).Google Scholar
[6]Macedońska-Nosalska, O., ‘The abelian case of Solitar's conjecture on infinite Nielsen transformations’, Canad. Math. Bull. 28 (1985), 223–230.CrossRefGoogle Scholar
[7]Magnus, W., Karrass, A. and Solitar, D., Combinatorial Group Theory (Interscience, New York, 1966).Google Scholar