On c-normal and hypercentrally embeded subgroups of finite groups

Ning Su, Yanming Wang

Abstract


In this article, we investigate the structure of a finite group \g under the assumption that some subgroups of \g are c-normal in $G$. The main theorem is as follows:

Let \e be a normal finite group of $G$. If all subgroups of \ep with order \dpp and 2\dpp (if $p=2$ and $E_{p}$ is not an abelian nor quaternion free 2-group) are c-normal in $G$, then \e is \phe $G$.

We give some applications of the theorem and generalize some known results.


Keywords


c-normal, hypercenter, p-supersolvable, p-nilpotent

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References


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