Characteristic Subgroups of Free Groups

Bryant, Roger M.

doi:10.1007/978-3-662-21571-5_11

Roger M. Bryant²

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 372))

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Abstract

In [4], B.H. Neumann asked whether it is true that every characteristic subgroup W of a free group F of infinite rank is fully invariant, and in [51 he conjectured that this is so. Cohen [1] provided support for the conjecture by proving that W is always fully invariant when F/W is abelian-by-nilpotent. However two examples will be described here of characteristic subgroups of the free group F of countable rank which are not fully invariant. Also, a proof will be given of the fact that there are continuously many characteristic subgroups of F which are not fully invariant.

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References

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Authors and Affiliations

UMIST, Manchester, M60 1QD, England
Roger M. Bryant

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Roger M. Bryant
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Editors and Affiliations

Dept. of Mathematics, Institute of Advanced Studies, Australian National University, 2600, Canberra, ACT, Australia
M. F. Newman

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Bryant, R.M. (1974). Characteristic Subgroups of Free Groups. In: Newman, M.F. (eds) Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21571-5_11

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DOI: https://doi.org/10.1007/978-3-662-21571-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06845-7
Online ISBN: 978-3-662-21571-5
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