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On Finitely Generated Subgroups of Free Products

Published online by Cambridge University Press:  09 April 2009

R. G. Burns
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If H is a subgroup of a group G we shall say that G is H-residually finite if for every element g in G, outside H, there is a subgroup of finite index in G, containing H and still avoiding g. (Then, according to the usual definition, G is residually finite if it is E-residually finite, where E is the identity subgroup). Definitions of other terms used below may be found in § 2 or in [6].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 3 , August 1971 , pp. 358 - 364
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Burns, R. G., ‘A note on free groups’, Proc. Amer. Math. Soc., 23 (1969), 14–17.CrossRefGoogle Scholar
[1]Dey, I. M. S., ‘Schreier systems in free products’, Proc. Glasgow Math. Assoc., 7 (1965–1966), 61–79.CrossRefGoogle Scholar
[3]Gruenberg, K. W., ‘Residual properties of infinite soluble groups’, Proc. London Math. Soc. (3) 7 (1957), 29–62.CrossRefGoogle Scholar
[4]Hall, M. Jr, ‘Coset representation in free groups’, Trans. Amer. Math. Soc. 67 (1949), 421–432.CrossRefGoogle Scholar
[5]MacLane, S., ‘A proof of the subgroup theorem for free products’, Mathematika 5 (1958), 161–183.CrossRefGoogle Scholar
[6]Magnus, W., Karrass, A. and Solitar, D., Combinatorial group theory (Interscience, New York, 1966).Google Scholar
[7]Karrass, A. and Solitar, D., ‘On finitely generated subgroups of a free group’, Proc. Amer. Math. Soc., 22 (1969), 209–213.CrossRefGoogle Scholar