# A note on free groups

@inproceedings{Burns1969ANO, title={A note on free groups}, author={Robert G. Burns}, year={1969} }

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], and Howson [4], follow as relatively easy corollaries of this stronger statement (Corollaries 2 and 3). Since the terminology is not fixed, we note for definiteness that by a right transversal for a subgroup H in a group G we shall mean a complete set of representatives of cosets Hg, gEFG. Other terms…

## 36 Citations

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This paper derives from a course in group theory which I gave at Berkeley in 1982. I wanted to prove the standard theorems on free groups, and discovered that, after a few preliminaries, the notion…

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Introduction: A theorem of Marshall Hall, Jr. [5] (cf. also [2], [4]) states that if B = {h1, ..., hk} is a free basis for a finitely generated subgroup H of a f.g. free group F , and if {x1, . . . ,…

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A well known theorem of Burns and Romanovskii states that a free product of subgroup separable groups is itself subgroup separable. We provide a proof using the language of immersions and coverings…

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