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RELATIVE ELEMENTARY ABELIAN GROUPS AND A CLASS OF EDGE-TRANSITIVE CAYLEY GRAPHS
Published online by Cambridge University Press: 20 November 2015
Abstract
Motivated by a problem of characterising a family of Cayley graphs, we study a class of finite groups $G$ which behave similarly to elementary abelian
$p$-groups with
$p$ prime, that is, there exists a subgroup
$N$ such that all elements of
$G\setminus N$ are conjugate or inverse-conjugate under
$\mathsf{Aut}(G)$. It is shown that such groups correspond to complete multipartite graphs which are normal edge-transitive Cayley graphs.
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- © 2015 Australian Mathematical Publishing Association Inc.
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