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.
Citation
Guo-An Diao. Mark Feighn. "The Grushko decomposition of a finite graph of finite rank free groups: an algorithm." Geom. Topol. 9 (4) 1835 - 1880, 2005. https://doi.org/10.2140/gt.2005.9.1835
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