关于自同构群的结构

On the Construction of Automorphism Groups

本文考虑群的自同构群,得到了DC_(4n),QD_(8n)及MC_(4q)的自同构群的结构,我们有:①若n≥3,则AutDC_(4n)≌HolC_(2n)②若n≥2,则An在QD_(8n)≌AutC_(4n)∝C_(2n)。③若q≡1(mod4),则AutMC_(4q)≌HolC_q。

In this paper, we consider the automorphism group of a group.The constructions of the automorphism groups of DC_(4n) and QD_(8n) areobtained. We obtain the following conclusion: (i) if n≥3, then AutDC_(4n)≌HolC_(2n), (ii) if n≥2 then Aut QD_(8n)≌AutC_(4n)∝C_(2n), (iii) prime q≡1(mod4)then AutMC_(4q)≌HolC_q.