p^n(n≤4)阶capable群

The Capable Groups of Order p^n(n≤ 4)

一个群G能够充当另外一个群H的中商群,称群G是capable群.考虑的问题是:对于阶为p^n(n≤4)的p-群G,哪些群是capable群?完全决定了p^n(n≤4)阶的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. In this paper, we investigate the following question： which p-groups of order p^n（n ≤ 4） are capable？ This paper determines completely the capable p-groups of order p^n（n ≤ 4）.