每个子群都c-正规的有限群

Finite groups in which every subgroup is c-normal

在本文中我们研究有限CN-群,即每个子群都c-正规的有限群.我们得到以下结果:群G是CN-群当且仅当G∈的每个子群都在G中正规.群G是CN-群当且仅当G可解且c-正规性是传递的.设p是一个奇素数,P是一个p-群,则P是一个CN-群当且仅当Φ(P)≤Z(P).我们也得到了一些CN-群的直积为CN-群的判别条件.

In this paper, we study the structure of finite CN-groups, which are groups with every subgroup c-normal. We obtain the following results： A group G is a CN-group if and only if each subgroup of G∈is normal in G. A group G is a CN-group if and only if the G is solvable and c-normality is transitive in G. Let P be a p-group where p is a odd prime. Then P is a CN-group if and only if Φ（P）≤Z（P）. We also get some criteria of CN-group in terms of direct product of CN-groups.