On Finitely Generated Subgroups of Free Products

@article{Burns1971OnFG,
  title={On Finitely Generated Subgroups of Free Products},
  author={Robert G. Burns},
  journal={Journal of The Australian Mathematical Society},
  year={1971},
  volume={12},
  pages={358-364}
}
  • Robert G. Burns
  • Published 1 August 1971
  • Mathematics
  • Journal of The Australian Mathematical Society
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The object of this note is to point out a theorem of M. Hall, Jr. (Theorem 1), proved, but formulated in a weaker form, as Theorem 5.1 of [2]. We then show that results of Karrass and Solitar [5],Expand
On finitely generated subgroups of a free product
1. Introduction. In [2], M. Hall, Jr. proved the following theorem: Let 77 be a finitely generated subgroup of a free group Fand suppose ßi, • • • , ßn are in F but no ßi is in 77. Then we mayExpand
Schreier systems in free products
In 1927 Schreier [8] proved the Nielsen-Schreier Theorem that a subgroup H of a free group F is a free group by selecting a left transversal for H in F possessing a certain cancellation property.Expand