On the supersolubility of a finite group with NS-supplemented Sylow subgroups

2019/01/14 by Monakhov, V. S., Trofimuk, A. A.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1901.04381

Abstract

A subgroup A of a group~G is said to be \sl NS-supplemented in G, if there exists a subgroup~B of G such that G=AB and whenever X~is a normal subgroup of~A and p∈ π(B), there exists a Sylow p-subgroup~B_p of~B such that XB_p=B_pX. In this paper, we proved the supersolubility of a group with NS-supplemented non-cyclic Sylow subgroups. The solubility of a group with NS-supplemented maximal subgroups is obtained.

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