On the partial Π-property of second minimal or second maximal subgroups of Sylow subgroups of finite groups.

AbstractLet <italic>H</italic> be a subgroup of a finite group <italic>G</italic>. We say that <italic>H</italic> satisfies the partial Π -property in <italic>G</italic> if there exists a chief series ΓG:1=G0<G1<···<Gn=G of <italic>G</italic> such that for every <italic>G</italic>-chief factor Gi/Gi−1 (1≤i≤n) of ΓG, |G/Gi−1:NG/Gi−1(HGi−1/Gi−1∩Gi/Gi−1)| is a π(HGi−1/Gi−1∩Gi/Gi−1) -number. In this paper, we study the influence of some second minimal or second maximal subgroups of a Sylow subgroup satisfying the partial Π -property on the structure of a finite group. [ABSTRACT FROM AUTHOR]