Finite groups with a cyclic norm quotient
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The norm $N(G)$ of a group $G$ is the intersection of the normalizers of all the subgroups of $G$. In this paper, the structure of finite groups with a cyclic norm quotient is determined. As an application of the result, an interesting characteristic of cyclic groups is given, which asserts that a finite group $G$ is cyclic if and only if ${\rm Aut}(G)/P(G)$ is cyclic, where $P(G)$ is the power automorphism group of $G$.
Abstract
The norm $N(G)$ of a group $G$ is the intersection of the normalizers of all the subgroups of $G$. In this paper, the structure of finite groups with a cyclic norm quotient is determined. As an application of the result, an interesting characteristic of cyclic groups is given, which asserts that a finite group $G$ is cyclic if and only if ${\rm Aut}(G)/P(G)$ is cyclic, where $P(G)$ is the power automorphism group of $G$.
참고문헌 (12)
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