极大类的capable 3-群

The capable 3-groups of maximal class

对于一个给定的群G,如果能有另外一个群H满足H/Z(H)■G,则称G是capable群,或称G可以充当中心商.对capable群的研究在p-群分类问题的研究中起着相当重要的作用.借助群的扩张理论,通过换位子计算,得到一些极大类3-群为capable群,并且由群G构造出了群H,使得H/Z(H)■G.

A group G was said to be capable if and only if G was isomorphic to H/Z(H)for some group H,where Z(H)was the center of H.The question of which p-groups were capable was interesting and played an important role in their classification.Throng cyclic extension theory and commutator calculation,the paper determined some capable 3-group G and construct H such that G was isomorphic to H/Z(H).