Volume 9, issue 4 (2005)

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

Guo-An Diao and Mark Feighn

Geometry & Topology 9 (2005) 1835–1880

arXiv: math.GR/0510198

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
Mathematical Subject Classification 2000
Primary: 20F65
Secondary: 20E05
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Publication
Received: 5 February 2005
Revised: 11 September 2005
Accepted: 7 August 2005
Published: 25 September 2005
Proposed: Benson Farb
Seconded: Martin Bridson, Joan Birman
Authors
Guo-An Diao
School of Arts and Sciences
Holy Family University
Philadelphia
Pennsylvania 19114
USA
Mark Feighn
Department of Mathematics and Computer Science
Rutgers University
Newark
New Jersey 07102
USA