Geometry & Topology, Vol. 9 (2005) Paper no. 41, pages 1835--1880.

The Grushko decomposition of a finite graph of finite rank free groups: an algorithm

Guo-An Diao, Mark Feighn

Abstract. A finitely generated group admits a decomposition, called its Grushko decomposition, into a free product of freely indecomposable groups. There is an algorithm to construct the Grushko decomposition of a finite graph of finite rank free groups. In particular, it is possible to decide if such a group is free.

Keywords. Graph of groups, Grushko decomposition, algorithm, labeled graph

AMS subject classification. Primary: 20F65. Secondary: 20E05.

E-print: arXiv:math.GR/0510198

DOI: 10.2140/gt.2005.9.1835

Submitted to GT on 5 February 2005. (Revised 11 September 2005.) Paper accepted 7 August 2005. Paper published 25 September 2005.

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Guo-An Diao, Mark Feighn
School of Arts and Sciences, Holy Family University
Philadelphia, PA 19114, USA
Department of Mathematics and Computer Science
Rutgers University, Newark, NJ 07102, USA

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