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The Compressed Word Problem for Groups pp 87–113Cite as

The Compressed Word Problem in Graph Products

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Abstract

In this chapter we will introduce an important operation in combinatorial group theory: graph products. A graph product is specified by a finite undirected graph, where every node is labeled with a group. The graph product specified by this group-labeled graph is obtained by taking the free product of all groups appearing in the graph, but elements from adjacent groups are allowed to commute. This operation generalizes free products as well as direct products. Graph groups were introduced by Green in her thesis [66]. Further results for graph products can be found in [51, 75, 83, 129].

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  1. Department for Electrical Engineering and Computer Science, University of Siegen, Siegen, Germany

    Markus Lohrey

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© 2014 Markus Lohrey

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Lohrey, M. (2014). The Compressed Word Problem in Graph Products. In: The Compressed Word Problem for Groups. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0748-9_5

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