Stallings foldings and subgroups of amalgams of finite groups

L. Markus-Epstein*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Stallings showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse automaton. This allows for the deep algorithmic theory of finite automata and finite inverse monoids to be used to answer questions about finitely generated subgroups of free groups. In this paper, we attempt to apply the same methods to other classes of groups. A fundamental new problem is that the Stallings folding algorithm must be modified to allow for "sewing" on relations of non-free groups. We look at the class of groups that are amalgams of finite groups. It is known that these groups are locally quasiconvex and thus, all finitely generated subgroups are represented by finite automata. We present an algorithm to compute such a finite automaton and use it to solve various algorithmic problems.

Original languageEnglish
Pages (from-to)1493-1535
Number of pages43
JournalInternational Journal of Algebra and Computation
Issue number8
StatePublished - Dec 2007
Externally publishedYes


  • Amalgamated free products
  • Labeled graphs
  • Membership problem
  • Subgroups


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