A criterion for a group to be nilpotent | Flowers | Note di Matematica

A criterion for a group to be nilpotent

Neil Flowers

Abstract

Let $G$ be a group with $|\pi(G)| \geq 3$ . In this paper it is shown that $G$ is nilpotent if and only if for every subgroup $H$ of $G$ with $|\pi(H)| \geq 2$ we have $P \cap H \in \mbox{Syl}_{p}(H)$ for each $P \in \mbox{Syl}_{p}(G)$ and for every $p \in \pi(G)$ .

DOI Code: 10.1285/i15900932v20n1p33

Keywords: Nilpotent; Sylow subgroups; Intersections of Sylow subgroups with subgroups

Classification: 20D15; 20D20

Full Text: PDF

کاغذ a4 ویزای استارتاپ

Creative Commons License

This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.