Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T16:13:25.833Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)