ISSN:
1420-8903
Keywords:
Primary 05C25
;
Secondary 05C30
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetG be a group generated by a subset of elementsS. The Cayley diagram ofG givenS is the labeled directed graph with vertices identified with the elements ofG and (v, u) is an edge labeledh ifh ∈S anduh=v. The sequence of elements ofS corresponding to the edges transversed in a hamiltonian path (whose initial vertex is the identity) is called a group generating sequence (abbreviatedggs) inS. In this paper a minimal upper bound for the number ofggs's in a pair of generator elements for any two-generated group is given. For all groups of the formG=〈a, b:b n =1,a m =b r ,ba=ab −1〉 wherem is even, it is shown that the number ofggs's in {a, b} is 1+m(n−1)/2. An algorithm is developed that yields the number ofggs's for two-generated groupsG=〈a, b〉 for which 〈ba −1〉⊲G. Explicit forms for the countedggs's are also provided.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02188014
Permalink
