Finite and infinite cyclic extensions of free groups
- 1 December 1973
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 16 (4) , 458-466
- https://doi.org/10.1017/s1446788700015445
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- On the Free Product of Two Groups with an Amalgamated Subgroup of Finite Index in each FactorProceedings of the American Mathematical Society, 1970
- The Subgroups of a Free Product of Two Groups with an Amalgamated SubgroupTransactions of the American Mathematical Society, 1970