The word problem and related results for graph product groups

Author:
K. J. Horadam

Journal:
Proc. Amer. Math. Soc. **82** (1981), 157-164

MSC:
Primary 20F10; Secondary 03D40, 05C25, 20L10

DOI:
https://doi.org/10.1090/S0002-9939-1981-0609643-1

MathSciNet review:
609643

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Abstract | References | Similar Articles | Additional Information

Abstract: A graph product is the fundamental group of a graph of groups. Amongst the simplest examples are HNN groups and free products with amalgamation.

The torsion and conjugacy theorems are proved for any group presented as a graph product. The graphs over which some graph product has a solvable word problem are characterised. Conditions are then given for the solvability of the word and order problems and also for the extended word problem for cyclic subgroups of any graph product. These results generalise the known ones for HNN groups and free products with amalgamation.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0609643-1

Keywords:
Groupoid,
graph of groups,
fundamental group,
word problem,
extended word problem,
torsion theorem,
conjugacy theorem

Article copyright:
© Copyright 1981
American Mathematical Society