On SS-quasinormal subgroups of finite groups (original) (raw)

Characterization of Finite Groups With Some S-quasinormal Subgroups

Monatshefte für Mathematik, 2005

A subgroup of a finite group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. In this paper we give a characterization of a finite group G under the assumption that every subgroup of the generalized Fitting subgroup of prime order is S-quasinormal in G.

The influence of SS-quasinormality of some subgroups on the structure of finite groups

Journal of Algebra, 2008

The following concept is introduced: a subgroup H of the group G is said to be SS-quasinormal (Supplement-Sylow-quasinormal) in G if H possesses a supplement B such that H permutes with every Sylow subgroup of B. Groups with certain SS-quasinormal subgroups of prime power order are studied. For example, fix a prime divisor p of |G| and a Sylow p-subgroup P of G, let d be the smallest generator number of P and M d (P ) denote a family of maximal subgroups P 1 , . . . , P d of P satisfying d i=1 (P i ) = Φ(P ), the Frattini subgroup of P . Assume that the group G is p-solvable and every member of some fixed M d (P ) is SS-quasinormal in G, then G is p-supersolvable.

Finite Groups with SS-Quasinormal Subgroups

International Journal of Algebra, 2010

A subgroup H of a group G is said to be SS-quasinormal (supplement-Sylow-quasinormal) in G if there is a supplement B of H to G such that H is permutable with every Sylow subgroup of B. In this paper we investigate the influence of SS-quasinormality of minimal subgroups or 2-minimal subgroups of finite group and extent the result of A. Carocca and some well-known results.

IRJET- On Some Minimal S-Quasinormal Subgroups of Finite Groups

IRJET, 2020

A subgroup H of a group G is permutable subgroup of G if for all subgroups S of G the following condition holds SH = HS < S,H >. A subgroup H is S-quasinormal in G if it permutes with every Sylow subgroup of G. In this article we study the influence of S-quasinormality of subgroups of some subgroups of G on the super-solvability of G.

On SS-quasinormal and S-quasinormally embedded subgroups of finite groups

Mathematical Notes, 2014

A subgroup H of a group G is said to be an SS-quasinormal (Supplement-Sylow-quasinormal) subgroup if there is a subgroup B of G such that HB = G and H permutes with every Sylow subgroup of B. A subgroup H of a group G is said to be S-quasinormally embedded in G if for every Sylow subgroup P of H, there is an S-quasinormal subgroup K in G such that P is also a Sylow subgroup of K. Groups with certain SS-quasinormal or S-quasinormally embedded subgroups of prime power order are studied.

S-quasinormallity of finite groups

Frontiers of Mathematics in China, 2010

Let d be the smallest generator number of a finite p-group P, and let M d (P ) = {P 1 , . . . , P d } be a set of maximal subgroups of P such that ∩ d i=1 P i = Φ(P ). In this paper, the structure of a finite group G under some assumptions on the S-quasinormally embedded or SS-quasinormal subgroups in M d (P ), for each prime p, and Sylow p-subgroups P of G is studied.

On S-quasinormally embedded subgroups of finite groups

Mathematical Notes, 2017

A subgroup H of a group G is said to be S-quasinormally embedded in G if for every Sylow subgroup P of H, there is an S-quasinormal subgroup K in G such that P is also a Sylow subgroup of K. Groups with certain S-quasinormally embedded subgroups of prime power order are studied. We prove Theorems 1.4, 1.5 and 1.6 of [10] remain valid if we omit the assumption that G is a group of odd order.

On s-quasinormal and c-normal subgroups of a finite group

Acta Mathematica Sinica, English Series, 2008

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On Quasi S-Propermutable Subgroups of Finite Groups

Journal of Mathematics, 2020

A subgroup H of a finite group G is said to be quasi S-propermutable in G if K ⊲ ¯ G such that H K is S-permutable in G and H ∩ K ≤ H q s G , where H q s G is the subgroup formed by all those subgroups of H which are S -propermutable in G . In this paper, we give some generalizations of finite group G by using the properties and effects of quasi S-propermutable subgroups.