منابع مشابه
Groups with Context-free Co-word Problem
The class of co-context-free groups is studied. A co-context-free group is defined as one whose coword problem (the complement of its word problem) is context-free. This class is larger than the subclass of context-free groups, being closed under the taking of finite direct products, restricted standard wreath products with context-free top groups, and passing to finitely generated subgroups an...
متن کاملLocal Similarity Groups with Context-free Co-word Problem
Let G be a group, and let S be a finite subset of G that generates G as a monoid. The co-word problem is the collection of words in the free monoid S that represent non-trivial elements of G. A current conjecture, based originally on a conjecture of Lehnert and modified into its current form by Bleak, Matucci, and Neuhöffer, says that Thompson’s group V is a universal group with context-free co...
متن کاملGroups with poly-context-free word problem
We consider the class of groups whose word problem is poly-contextfree; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free groups has poly-context-free word problem, and conjecture that the converse also holds. We prove our conjecture for several classes of soluble groups, includin...
متن کاملGroups with Indexed Co-word Problem
We investigate co-indexed groups, that is groups whose co-word problem (all words defining nontrivial elements) is an indexed language. We show that all Higman-Thompson groups and a large class of tree automorphism groups defined by finite automata are co-indexed groups. The latter class is closely related to dynamical systems and includes the Grigorchuk 2-group and the Gupta-Sidki 3-group. The...
متن کاملContext-Freeness of Higman-Thompson group’s co-word problem
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...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2005
ISSN: 0024-6107,1469-7750
DOI: 10.1112/s002461070500654x