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Groups with indexed co-word problem
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Holt, Derek F. and Roever, Claas E. (2006) Groups with indexed co-word problem. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 16 (5). pp. 985-1014. doi:10.1142/S0218196706003359 ISSN 0218-1967.
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Abstract
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 co-word problems of all these examples are in fact accepted by nested stack automata with certain additional properties, and we establish various closure properties of this restricted class of co-indexed groups, including closure under free products.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | ||||
Publisher: | WORLD SCIENTIFIC PUBL CO PTE LTD | ||||
ISSN: | 0218-1967 | ||||
Official Date: | October 2006 | ||||
Dates: |
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Volume: | 16 | ||||
Number: | 5 | ||||
Number of Pages: | 30 | ||||
Page Range: | pp. 985-1014 | ||||
DOI: | 10.1142/S0218196706003359 | ||||
Publication Status: | Published |
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