A criterion for a group to be nilpotent


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

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