Geodesic
Subgroups of HNN Groups and Groups with one Defining Relation
Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 627-643

Voir la notice de l'article provenant de la source Cambridge University Press

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 {φ i } is a collection of isomorphisms of subgroups {L i} 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. 
Karrass, A.; Solitar, D. Subgroups of HNN Groups and Groups with one Defining Relation. Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 627-643. doi: 10.4153/CJM-1971-070-x
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[1] 1. Baumslag, G., On generalized free products of torsion-free nilpotent groups. I (to appear in Illinois J. Math.). Google Scholar

[2] 2. Baumslag, G., Karrass, A. and Solitar, D., Torsion-free groups and amalgamated products, Proc. Amer. Math. Soc. 24 (1970), 688–690. Google Scholar

[3] 3. Britton, J. L., The word problem, Ann. of Math. 84 (1963), 16–32. Google Scholar

[4] 4. Higman, G., Subgroups of finitely presented groups, Proc. Roy. Soc. London Ser. A 262 (1961), 455–475. Google Scholar

[5] 5. Higman, G., Neumann, B. H. and Neumann, H., Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247–254. Google Scholar

[6] 6. Karrass, A. and Solitar, D., The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 149 (1970), 227–255. Google Scholar

[7] 7. Magnus, W., Karrass, A. and Solitar, D., Combinatorial group theory, Pure and Appl. Math., Vol. 13 (Interscience, New York 1966). Google Scholar

[8] 8. Moldavanski, D. I., Certain subgroups of groups with one defining relation, Siberian Math. J. 8 (1967), 1370–1384. Google Scholar

[9] 9. Newman, B. B., Some aspects of one relator groups (to appear). Google Scholar

[10] 10. Neumann, B. H., An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. London Ser. A 246 (1954), 503–554. Google Scholar

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