拟极小外p-自同构不动点子群为p阶的p-群

阶为某素数p的方幂的自同构如果不是内自同构,则称其为外p-自同构.如果φ是群G的外p-自同构且o(φ)=p,其中φ是φ在Out(G)=Aut(G)/Inn(G)中的自然同态像,则称φ为群G的拟极小外p-自同构.设φ是有限p-群G的任意拟极小外p-自同构,给出了|C_G(φ)|≤p时G的结构.

P-groups in Which the Centralizer of Each Quasi Minimal Noninner p-Automorphism Is of Order p

An automorphism of a group is called noninner p-automorphism if it is not an inner automorphism and its order is a power of p.Let φ be a noninner p-automorphism of G,then φ is called quasi minimal noninner p-automorphism if o(φ) = p,where φis the natural homomorphic image of φ in Out{G) = Aut(G)/Inn(G).In this note,it is proved that for every quasi minimal noninner p-automorphism φ of G,the subgroup Cg(φ) has order p if and only if G is order p~2.