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Residual properties of free groups II

Published online by Cambridge University Press:  17 April 2009

Stephen J. Pride
Stephen J. Pride
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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In this paper it is proved that non-abelian free groups are residually (x, y | xm = 1, yn = 1, xk = yh} if and only if min{(m, k), (n, h)} is greater than 1, and not both of (m, k) and (n, h) are 2 (where 0 is taken as greater than any natural number). The proof makes use of a result, possibly of independent interest, concerning the existence of certain automorphisms of the free group of rank two. A useful criterion which enables one to prove that non-abelian free groups are residually G for a large number of groups G is also given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 1 , August 1972 , pp. 113 - 120
Copyright
Copyright © Australian Mathematical Society 1972

References

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