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Finite and infinite cyclic extensions of free groups

Published online by Cambridge University Press:  09 April 2009

A. Karrass ,
A. Pietrowski  and
D. Solitar
A. Karrass
Affiliation:
York UniversityToronto Ontario, Canada
A. Pietrowski
Affiliation:
York UniversityToronto Ontario, Canada
D. Solitar
Affiliation:
York UniversityToronto Ontario, Canada
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Using Stalling's characterization [11] of finitely generated (f. g.) groups with infinitely many ends, and subgroup theorems for generalized free products and HNN groups (see [9], [5], and [7]), we give (in Theorem 1) a n.a.s.c. for a f.g. group to be a finite extension of a free group. Specifically (using the terminology extension of and notation of [5]), a f.g. group G is a finite extension of a free group if and only if G is an HNN group where K is a tree product of a finite number of finite groups (the vertices of K), and each (associated) subgroup Li, Mi is a subgroup of a vertex of K.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 4 , December 1973 , pp. 458 - 466
Copyright
Copyright © Australian Mathematical Society 1973

References

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