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A problem of Hanna Neumann on closed sets of group words

Published online by Cambridge University Press:  17 April 2009

L.G. Kovács  and
M.R. Vaughan-Lee
L.G. Kovács
Affiliation:
Institute of Advances Studies, Australian National University, Canberra, ACT.
M.R. Vaughan-Lee
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
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Abstract

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In Problem 1 of her book Varieties of groups, Hanna Neumann asked whether a fully invariant subsemigroup of a free group of infinite rank is necessarily a subgroup. This note presents an example which shows that the answer is negative.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 3 , December 1971 , pp. 341 - 342
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Neumann, Hanna, Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar