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The co‐word problem for the Higman‐Thompson group is context‐free
Author(s) -
Lehnert J.,
Schweitzer P.
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdl043
Subject(s) - word (group theory) , word problem (mathematics education) , mathematics , group (periodic table) , context (archaeology) , permutation (music) , combinatorics , set (abstract data type) , class (philosophy) , permutation group , arithmetic , artificial intelligence , computer science , history , chemistry , geometry , organic chemistry , programming language , physics , archaeology , acoustics
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 show that a permutation group has context‐free co‐word problem. This method is used 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 have an easier co‐word problem. We call this property semi‐deterministic context‐free . The second Houghton group belongs to this class.