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Intersections of finitely generated free groups

Published online by Cambridge University Press:  17 April 2009

Peter Nickolas
Peter Nickolas
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland 4067, Australia.
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Abstract

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A result of Howson is that two finitely generated subgroups U and V of a free group have finitely generated intersection. Hanna Neumann showed further that, if m, n and N are the ranks of U, V and U ∩ V respectively, then N ≤ 2(m−1)(n−1) + 1, and Burns strengthened this, showing that N ≤ 2(m−1)(n−1) − m + 2 (if m ≤ n). This paper presents a new and simple proof of Burns' result. Further, the graph-theoretical ideas used provide still stronger bounds in certain special cases.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 3 , June 1985 , pp. 339 - 348
Copyright
Copyright © Australian Mathematical Society 1985

References

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