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THE TWO-ARC-TRANSITIVE GRAPHS OF SQUARE-FREE ORDER ADMITTING ALTERNATING OR SYMMETRIC GROUPS

Part of: Permutation groups

Published online by Cambridge University Press:  29 March 2017

GAI XIA WANG  and
ZAI PING LU
GAI XIA WANG*
Affiliation:
Department of Applied Mathematics, AnHui University of Technology, Ma’an shan 243002, PR China email [email protected]
ZAI PING LU
Affiliation:
Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China email [email protected]
*
✉[email protected]
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Abstract

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Let $G$ be a finite group with $\mathsf{soc}(G)=\text{A}_{c}$ for $c\geq 5$. A characterization of the subgroups with square-free index in $G$ is given. Also, it is shown that a $(G,2)$-arc-transitive graph of square-free order is isomorphic to a complete graph, a complete bipartite graph with a matching deleted or one of $11$ other graphs.

Keywords

symmetric graphtwo-arc-transitive graphautomorphism group

MSC classification

Primary: 20B15: Primitive groups
Secondary: 20B30: Symmetric groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 104 , Issue 1 , February 2018 , pp. 127 - 144
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

This work is supported by National Natural Science Foundation of China (11371204) and NNSFC (11601005).

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