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FINITE CI-GROUPS ARE SOLUBLE

Published online by Cambridge University Press:  01 July 1999

CAI HENG LI
CAI HENG LI
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, WA 6907, Australia
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Abstract

For a finite group G and a subset S of G with 1∉S and S = S−1, the Cayley graph Cay(G, S) is the graph with vertex set G such that {x, y} is an edge if and only if yx−1∈S. The group G is called a CI-group if, for all subsets S and T of G[setmn ]{1}, Cay(G, S) ≅ Cay(G, T) if and only if Sσ = T for some σ∈Aut(G). In this paper, for each prime p ≡ 1 (mod 4), a symmetric graph Γ(p) is constructed from PSL(2, p) such that Aut Γ(p) = ℤ2 × PSL(2, p); it is then shown that A5 is not a CI-group, and that all finite CI-groups are soluble.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 4 , July 1999 , pp. 419 - 423
Copyright
© The London Mathematical Society 1999

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