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An alternative proof that the Fibonacci group \(F(2,9)\) is infinite. (English) Zbl 0853.20019

Summary: This note contains a report of a proof by computer that the Fibonacci group \(F(2,9)\) is automatic. The automatic structure can be used to solve the word problem in the group. Furthermore, it can be seen directly from the word-acceptor that the group generators have infinite order, which of course implies that the group itself is infinite.

MSC:

20F05 Generators, relations, and presentations of groups
20F65 Geometric group theory
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20-04 Software, source code, etc. for problems pertaining to group theory

Software:

AUTOMATA
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References:

[1] Holt D. F., J. Symb. Comp. 12 pp 397– (1991) · Zbl 0779.20017
[2] Epstein D. B. A., Word Processing and Group Theory (1992)
[3] Havas G., Proc. Roy. Soc. Edinburgh 83 pp 199– (1979) · Zbl 0416.20026
[4] Helling H., ”On Fibonacci groups” · Zbl 0189.09902
[5] Derek Holt F., ”The Warwick Automatic Groups Software” (1994) · Zbl 0932.20037
[6] DOI: 10.1017/CBO9780511629303
[7] DOI: 10.1007/BF01188513 · Zbl 0662.20023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.