On a question of B. H. Neumann
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- by Robert Guralnick and Igor Pak PDF
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Abstract:
The automorphism group of a free group $\operatorname {Aut}(F_k)$ acts on the set of generating $k$-tuples $(g_1,\dots ,g_k)$ of a group $G$. Higman showed that when $k=2$, the union of conjugacy classes of the commutators $[g_1,g_2]$ and $[g_2,g_1]$ is an orbit invariant. We give a negative answer to a question of B.H. Neumann, as to whether there is a generalization of Higman’s result for $k \ge 3$.References
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Additional Information
- Robert Guralnick
- Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113
- MR Author ID: 78455
- Email: guralnic@math.usc.edu
- Igor Pak
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307
- MR Author ID: 293184
- ORCID: 0000-0001-8579-7239
- Received by editor(s): June 1, 2001
- Received by editor(s) in revised form: February 20, 2002
- Published electronically: December 30, 2002
- Communicated by: Stephen D. Smith
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2021-2025
- MSC (2000): Primary 20D60
- DOI: https://doi.org/10.1090/S0002-9939-02-06752-7
- MathSciNet review: 1963745