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Subgroups of HNN Groups and Groups with one Defining Relation
- Source :
- Canadian Journal of Mathematics. 23:627-643
- Publication Year :
- 1971
- Publisher :
- Canadian Mathematical Society, 1971.
-
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 group1the 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.
- Subjects :
- Group (mathematics)
General Mathematics
010102 general mathematics
01 natural sciences
Base (group theory)
Combinatorics
Tree (descriptive set theory)
Product (mathematics)
0103 physical sciences
010307 mathematical physics
0101 mathematics
Relation (history of concept)
Mathematics
Structured program theorem
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 23
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........b619e91a6c104ffa67869f86990eaf1b