论文标题
有限的DC组
Finite DC-groups
论文作者
论文摘要
令G为组，DS（G）= {H'| H是G}的任何子组。如果ds（g）是链条，则g被认为是DC组。在本文中，我们证明有限的DC组是Sylow p-Subgroup和Abelian P'-Subgroup的半领产品。对于G是有限的P组的情况，我们获得了DC组的一些特性。特别是，DC 2组的表征。此外，我们证明DC组是P <5的Metabelian，并举一个例子：对于P> 3而言，非亚洲DC组不一定是Metabelian。
Let G be a group and DS(G) = { H'| H is any subgroup of G}. G is said to be a DC-group if DS(G) is a chain. In this paper, we prove that a finite DC-group is a semidirect product of a Sylow p-subgroup and an abelian p'-subgroup. For the case of G being a finite p-group, we obtain some properties of a DC-group. In particular, a DC 2-group is characterized. Moreover, we prove that DC-groups are metabelian for p<5 and give an example that a non-abelian DC-group is not be necessarily metabelian for p>3.
