Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a question of B. H. Neumann


Authors: Robert Guralnick and Igor Pak
Journal: Proc. Amer. Math. Soc. 131 (2003), 2021-2025
MSC (2000): Primary 20D60
DOI: https://doi.org/10.1090/S0002-9939-02-06752-7
Published electronically: December 30, 2002
MathSciNet review: 1963745
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The automorphism group of a free group $\mathrm{Aut}(F_k)$ 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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20D60

Retrieve articles in all journals with MSC (2000): 20D60


Additional Information

Robert Guralnick
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113
Email: guralnic@math.usc.edu

Igor Pak
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307

DOI: https://doi.org/10.1090/S0002-9939-02-06752-7
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
Article copyright: © Copyright 2002 American Mathematical Society