内亚循环capable群性质研究

Property of inner-metacyclic capable group

本文研究了内亚循环p-群G满足capable群的条件,得到了这类群为capable p-群的充要条件。并由内亚循环p-群G构造得出了群H,满足H/Z(H)同构于G。

We address the conditions that an inner-metacyclic p-group is a capable group. We also acquire the necessary and sufficient conditions that an inner-metacyclic group is a capable p-group. We further construct a group H from an inner-metacyclic p-group G, which makes G isomorphic to H/Z（H）.