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 . We then show that results of Karrass and Solitar , and Howson , 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
Topology of finite graphs
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
The finite basis extension property and graph groups
• Mathematics
• 1990
Introduction: A theorem of Marshall Hall, Jr.  (cf. also , ) 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, . . . ,
Intersections of finitely generated free groups
• P. Nickolas
• Mathematics
Bulletin of the Australian Mathematical Society
• 1985
A result of Howson is that two finitely generated subgroups U and V of a free group have finitely generated intersection. Hanna Neumann showed further that, if m, n and N are the ranks of U, V and U
Virtual Retraction Properties in Groups
If \$G\$ is a group, a virtual retract of \$G\$ is a subgroup which is a retract of a finite index subgroup. Most of the paper focuses on two group properties: property (LR), that all finitely generated
On the rank of the intersection of subgroups of a fuchsian group
The Fuchsian groups are the discrete subgroups of LF(2, R), the group of all 2 × 2 matrices over the reels with determinant +1. We are interested here in the following group-theoretical property in
Graphs, free groups and the Hanna Neumann conjecture
Abstract A new bound for the rank of the intersection of finitely generated subgroups of a free group is given, formulated in topological terms, and in the spirit of Stallings [J. R. Stallings.
Ju n 20 06 Galois theory , graphs and free groups
A self-contained exposition is given of the topological and Galois-theoretic properties of the category of combinatorial1-complexes, or graphs, very much in the spirit of Stallings [ 20]. A number of
A Bass--Serre theoretic proof of a theorem of Burns and Romanovskii
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
The Combinatorial Topology of Groups
This is the first installment of a book on combinatorial and geometric group theory from the topological point of view. This is a classical subject. The installment contains Chapters 1, 3 and 4, and
Conjugacy Separability of Amalgamated Free Products of Groups
• Mathematics
• 1996
A group G is said to be conjugacy separable if any two elements x and y of G, whose images are conjugate in every finite quotient of G, are conjugate in G. The importance of this notion was pointed