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Subgroups of HNN Groups and Groups with one Defining Relation

Published online by Cambridge University Press:  20 November 2018

A. Karrass  and
D. Solitar
A. Karrass
Affiliation:
York University, Toronto, Ontario
D. Solitar
Affiliation:
York University, Toronto, Ontario
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HNN groups have appeared in several papers, e.g., [3; 4; 5; 6; 8]. In this paper we use the results in [6] to obtain a structure theorem for the subgroups of an HNN group and give several applications.

We shall use the terminology and notation of [6]. In particular, if K is a group and {φi} is a collection of isomorphisms of subgroups {Li} into K, then we call the group

1

the HNN group with base K, associated subgroups { Li,φi(Li)} and free part the group generated by t1, t2, …. (We usually denote φi(Li) by Mi or L–i.) The notion of a tree product as defined in [6] will also be needed.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 4 , August 1971 , pp. 627 - 643
Copyright
Copyright © Canadian Mathematical Society 1971

References

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