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.


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


Full Text: DOI arXiv EuDML EMIS


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[6] DOI: 10.1017/CBO9780511629303
[7] DOI: 10.1007/BF01188513 · Zbl 0662.20023
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