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A Note on Fibonacci Type Groups

Published online by Cambridge University Press:  20 November 2018

C. M. Campbell  and
E. F. Robertson
C. M. Campbell
Affiliation:
Mathematical Institute, University of St. Andrews, St. Andrews, KYI6 9SS, Scotland
E. F. Robertson
Affiliation:
Mathematical Institute, University of St. Andrews, St. Andrews, KYI6 9SS, Scotland
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Let Fn 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 Fn 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).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 173 - 175
Copyright
Copyright © Canadian Mathematical Society 1975

References

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