一些特殊的capable群

On Some Special Capable Groups

若存在一个群H,使得H/Z(H)同构于群G,则称群G为capable群.对capable群的研究在p-群的分类问题中起着至关重要的作用.运用群的循环扩张理论,通过换位子计算可以得到与Baer关于交换的capable群G完全一致的结果.

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 thecenter of H. The question of which p-groups are capable is interesting and plays an important role in their classification. Using theextension theory and calculating commutators can give the same conclusion about the abelian capable groups which the Baer hadstudied.