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Automorphism groups of semidirect products

Authors:	Fang Zhou Heguo Liu

Institution:	(1) Department of Mathematics, Hubei University, Wuhan, Hubei, 430062, P.R. China

Abstract:	This paper shows that if $G = H \rtimes K$ is a semidirect product of finite groups, then ${\rm Aut}G = C_{{\rm Aut}G}(H) C_{{\rm Aut}G}(K)$ if and only if $\theta(K) \cap H = 1$ and $K,\theta]\,\subseteq\,C_{G}(H)$ for all $\theta\,\in \, {\rm Aut}G$ . As an application, we investigate the automorphism group of a split metacyclic p-group for odd p. The second author is supported by the Natural Science Foundation of China (10671058).

Keywords:	Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 20E36 Secondary 20D45
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