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Some groups all of whose proper verbal quotients are relatively free

Published online by Cambridge University Press:  17 April 2009

Graham Higman
Graham Higman
Affiliation:
Mathematical Institute, 24–29 St Giles, Oxford OX1 3LB England
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Abstract

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A class of blocking pairs (A, B) for which B/AB is infinite cyclic is constructed and these are used to construct groups all of whose proper verbal quotients are relatively free.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 2 , October 1989 , pp. 231 - 234
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Baumslag, Gilbert, ‘More groups that are just about free’, Bull. Amer. Math. Soc. 74 (1968).CrossRefGoogle Scholar
[2]Baumslag, Gilbert and Stammbach, Urs, ‘A non-free parafree group all of whose countable subgroups are free’, Math. Z. 148 (1976).CrossRefGoogle Scholar
[3]Dunwoody, M.J., ‘Review of [1], MR 37 # 1449’.Google Scholar
[4]Iligman, Graham, ‘Some countably free groups’, in Group Theory, Proceedings of the Singapore International Conference, Editors Cheng, K.N. and Leong, Y.K. (De Gruyter, 1989).Google Scholar