Subgroups of HNN Groups and Groups with one Defining Relation
- 1 August 1971
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 23 (4) , 627-643
- https://doi.org/10.4153/cjm-1971-070-x
Abstract
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.Keywords
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