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Closure properties in the class of multiple context-free groups

Robert P. Kropholler EMAIL logo and Davide Spriano


We show that the class of groups with k-multiple context-free word problem is closed under graphs of groups with finite edge groups.

MSC 2010: 20F10; 68Q45

Award Identifier / Grant number: DMS-1440140

Funding statement: This work was started at MSRI, Berkeley, where research is supported by the National Science Foundation under Grant No. DMS-1440140.


We greatly thank Bob Gilman for introducing us to the subject and making this project possible. The second author would like to thank UC Berkeley for inviting him as a visiting scholar. The first author would like to thank Alessandro Sisto for inviting him to complete this work at the ETH. We thank the anonymous referee for helpful comments and suggestions, in particular, the addition of Section 6. Finally, we would like to thank Neil Fullarton for his invaluable work with a stapler.


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Received: 2018-05-22
Published Online: 2019-04-30
Published in Print: 2019-05-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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