Finite Groups with Minimal CSS-subgroups (original) (raw)
2021, European Journal of Pure and Applied Mathematics
Let G be a finite group. A subgroup H of G is called SS-quasinormal in G if there is a supplement B of H to G such that H permutes with every Sylow subgroup of B. A subgroup H of G is called CSS-subgroup in G if there exists a normal subgroup K of G such that G = HK and H ∩K is SS-quasinormal in G. In this paper, we investigate the influence of minimal CSS-subgroups of G on its structure. Our results improve and generalize several recent results in the literature.
Sign up for access to the world's latest research.
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Related papers
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.
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.
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.
Finite Groups Whose Minimal Subgroups are Weakly -SUBGROUPS
Acta Mathematica Scientia, 2012
Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG(H)∩H g ≤ H for all g ∈ G. A subgroup H of G is called a weakly H *-subgroup in G if there exists a subgroup K of G such that G = HK and H ∩ K is an H-subgroup in G. We investigate the structure of the finite group G under the assumption that every cyclic subgroup of G of prime order p or of order 4 (if p = 2) is a weakly H *-subgroup in G. Our results improve and extend a series of recent results in the literature. following concept: A subgroup H of a group G is called c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ H G. Also, in 2000, Bianchi et al. [4] introduced the concept of an H-subgroup as follows: A subgroup H of a group G is called an H-subgroup if N G (H) ∩ H g ≤ H for all g ∈ G. Recently, in 2012, Asaad, Heliel and Al-Shomrani [2] introduced a new concept, called a weakly H-subgroup, as follows: A subgroup H of a group G is called a weakly H-subgroup in G if there
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.
On s-quasinormal and c-normal subgroups of a finite group
Acta Mathematica Sinica, English Series, 2008
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
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.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.