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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

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Volume 12, Issue 3


Subgroups of free groups generated by conjugates of powers of the generators

Stephen P. Humphries
Published Online: 2008-11-06 | DOI: https://doi.org/10.1515/JGT.2008.090


For a free group Fn = 〈x 1, . . . , xn 〉 we investigate when a finite index subgroup of Fn is generated by a set 𝒳 of powers of conjugates of the generators x 1, . . . , xn . For the braid group Bn = 〈σ1, . . . , σn–1〉 we similarly consider when a finite index subgroup is generated by a set of powers of Dehn twists, i.e., conjugates of the elements . We indicate a connection of these problems with the theory of c-groups developed by Burnside, Schur and Wielandt.

About the article

Received: 2008-03-16

Revised: 2008-05-27

Published Online: 2008-11-06

Published in Print: 2009-05-01

Citation Information: Journal of Group Theory, Volume 12, Issue 3, Pages 465–485, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/JGT.2008.090.

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