Geodesic
A Note on Fibonacci Type Groups
Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 173-175

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Let F n be the free group on {ai:i ∊ Z n} where the set of congruence classes mod n is used as an index set for the generators. The permutation (1, 2, 3, ..., n) of Zn induces an automorphism θ of F n by permuting the subscripts of the generators. Suppose w is a word in Fn and let N(w) denote the normal closure of {wθi-1:l ≤i≤n}. Define the group Gn(w) by Gn(w)=Fn/N(w) and call wdi-1=l the relation (i) of Gn(w). 
Campbell, C. M.; Robertson, E. F. A Note on Fibonacci Type Groups. Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 173-175. doi: 10.4153/CMB-1975-034-7
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     title = {A {Note} on {Fibonacci} {Type} {Groups}},
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     year = {1975},
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