亚循环的Capable p-群

The Metacyclic Capable p-Groups

给定了一个群G,若存在另外的一个群H,能够使得H/Z(H)≌G,则称G是capable群.对cable群进行研究在p-群分类问题的研究中起着相当重要的作用.完全决定了亚循环的capable p-群G.

A group G is said to be capable if and only if G is isomorphic to H/Z（H） for some group H, where Z（H） is the center of H. The question of which p-groups are capable is interesting and plays an important role in their classification. This paper determines completely the metacyclic capable p-groups.