On finite groups with a certain sylow normalizer. I

Finite Groups with p-Sylow Coverings

finite groups with p-sylow coverings

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Normalizer of Sylow Subgroups and the Structure of a Finite Group

In this paper, we prove the p-nilpotency of a finite group with assumption that some subgroups of Sylow subgroup are weakly s-semipermutable subgroups in the normalizer of Sylow subgroups. Our results unify and generalize some earlier results. Mathematics Subject Classification: 20D10, 20D15

POS-groups with some cyclic Sylow subgroups

A finite group G is said to be a POS-group if for each x in G the cardinality of the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups with some cyclic Sylow subgroups.