On metacyclic Fibonacci groups

Colin Matthew Campbell, E. F. Robertson · Proceedings of the Edinburgh Mathematical Society · 1975

Let Fn be the free group on {ai: i ∈ Zn}, where the set of congruence classes mod n is used as an index set for the generators. Let φ be the permutation (1, 2, 3, …, n) of Zn and denote by θ the automorphism of Fn induced by φ, namely

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