Abstract
The set of left multiplications by the elements of a group G form a subgroup LG of the automorphism group A(X) for any Cayley graph X of G. The Cayley index c(G) of G is the minimum of the index [A(X) : LG] taken over all Cayley graphs X of G. The present article is expository, reporting what is known to date about Cayley indices of groups and where some of the results may be found. The general pattern thus far indicates that, with finitely many exceptions, c(G) is determined by whether G is (1) abelian, (2) generalized dicyclic, (3) solvable and finite but neither abelian nor generalized dicyclic, or (4) none of the above.
Keywords
- Abelian Group
- Automorphism Group
- Cayley Graph
- Free Product
- Solvable Group
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© 1978 Springer-Verlag
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Watkins, M.E. (1978). On the cayley index of a group. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062521
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DOI: https://doi.org/10.1007/BFb0062521
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