AUTOMORPHISM GROUPS OF 4-VALENT CONNECTED CAYLEY GRAPHS OF p-GROUPS |
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Authors: | FENG Yanquan Jin Ho KWAK WANG Ruji |
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Affiliation: | 1. Department of Mathematics, Northern Jiaotong University, 2. Department of Mathematics, 3. Department of Mathematics, Capital Normal University, |
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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 Ant(X) of X is isomorphic to the semidirect product GR x Ant(G,S), where GR 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. |
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Keywords: | Cayley graphs Normal Cayley graphs Automorphism groups |
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