Groups Whose Word Problem is a Petri Net Language
There has been considerable interest in exploring the connections between the word problem of a finitely generated group as a formal language and the algebraic structure of the group. However, there are few complete characterizations that tell us precisely which groups have their word problem in a specified class of languages. We investigate which finitely generated groups have their word problem equal to a language accepted by a Petri net and give a complete classification, showing that a group has such a word problem if and only if it is virtually abelian.
KeywordsFinitely generated group Word problem Petri net language
Some of the research for this paper was done whilst the authors were visiting the Nesin Mathematics Village in Turkey; the authors would like to thank the Village both for the financial support that enabled them to work there and for the wonderful research environment it provided that stimulated the results presented here. The authors would like to thank the referees for their helpful and constructive comments. The second author also would like to thank Hilary Craig for all her help and encouragement.
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