Displaying similar documents to “On E-S-supplemented subgroups of finite groups”

On supplements of subgroups of finite groups

Xianhua Li, A. Ballester-Bolinches (2006)

Bollettino dell'Unione Matematica Italiana


In this paper the concept of s-pair for a subgroup of a finite group is introduced and studied. It provides a uniform way to study the influence of some families of subgroups on the structure of a finite group. A criterion for a finite group to belong to a saturated formation and necessary and sufficient conditions for solubility, supersolvability and nilpotence of a finite group are given.

Pronormal and subnormal subgroups and permutability

James Beidleman, Hermann Heineken (2003)

Bollettino dell'Unione Matematica Italiana


We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow p -subgroups for p < 7 permute with all subnormal subgroups.

On Groups whose Contranormal Subgroups are Normally Complemented

Kurdachenko, L. A., Subbotin, I. Ya. (2011)

Serdica Mathematical Journal


2000 Mathematics Subject Classification: 20F16, 20E15. Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.

Conditions for p-supersolubility and p-nilpotency of finite soluble groups

Wenai Yan, Baojun Li, Zhirang Zhang (2013)

Colloquium Mathematicae


Let ℨ be a complete set of Sylow subgroups of a group G. A subgroup H of G is called ℨ-permutably embedded in G if every Sylow subgroup of H is also a Sylow subgroup of some ℨ-permutable subgroup of G. By using this concept, we obtain some new criteria of p-supersolubility and p-nilpotency of a finite group.