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| AUTOMORPHISM GROUPS OF 4-VALENT CONNECTED CAYLEY GRAPHS OF p-GROUPS |
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Citation： |
FENG Yanquan,Jin Ho KWAK,WANG Ruji.AUTOMORPHISM GROUPS OF 4-VALENT CONNECTED CAYLEY GRAPHS OF p-GROUPS[J].Chinese Annals of Mathematics B,2001,22(3):281~286 |
| Page view： 1339
Net amount： 844 |
Authors： |
FENG Yanquan; Jin Ho KWAK;WANG Ruji |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10071002) and
Com2MaC-KOSEF. |
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| Abstract： |
Let $G$ be a $p$-group ($p$ odd prime) and let $X=\Cay(G,S)$ be a
$4$-valent connected Cayley graph. It is shown that if $G$ has
nilpotent class $2$, then the automorphism group $\Aut(X)$ of $X$
is isomorphic to the semidirect product $G_R\rtimes \Aut(G,S)$,
where $G_R$ is the right regular representation of $G$ and
$\Aut(G,S)$ is the subgroup of the automorphism group $\Aut(G)$ of
$G$ which fixes $S$ setwise. However the result is not true if $G$
has nilpotent class $3$ and this paper provides a counterexample. |
Keywords： |
Cayley graphs, Normal Cayley graphs, Automorphism groups |
Classification： |
05C25, 20B25 |
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