Geodesic
An Improved Subgroup Theorem for HNN Groups with Some Applications
Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 214-224

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In [4], a subgroup theorem for HNN groups was established. The theorem was proved by embedding the given HNN group in a free product with amalgamated subgroup and then applying the subgroup theorem of [3]. In this paper we obtain a sharper form of the subgroup theorem of [4] by applying the Reidemeister-Schreier method directly, using an appropriate Schreier system of coset representatives. Specifically, we prove (in Theorem 1) that if H is a subgroup of the HNN group 1 
Karrass, A.; Pietrowski, A.; Solitar, D. An Improved Subgroup Theorem for HNN Groups with Some Applications. Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 214-224. doi: 10.4153/CJM-1974-021-1
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