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Context-Freeness of Higman-Thompson group's co-word problem

Joerg Lehnert·Pascal Schweitzer
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Abstract

The co-word problem of a group G generated by a set X is defined as the set of words in X which do not represent 1 in G. We introduce a new method to decide if a permutation group has context-free co-word problem. We use this method to show, that the Higman-Thompson groups, and therefore the Houghton groups, have context-free co-word problem. We also give some examples of groups, that even have an easier co-word problem. We call this property semi-deterministic context-free. The second Houghton group belongs to this class.

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Joerg Lehnert, Pascal Schweitzer. 2005-07-05. Context-Freeness of Higman-Thompson group's co-word problem. https://arxiv.org/abs/math/0507090

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