A subgroup H of G is said to be c-normal in G if there exists a normal subgroup N of G such that HN = G and H ∩ N ≤ H G  = Core(H). We extend the study on the structure of a finite group under the assumption that all maximal or minimal subgroups of the Sylow subgroups of the generalized Fitting subgroup of some normal subgroup of G are c-normal in G. The main theorems we proved in this paper are: Theorem Let ℱ be a saturated formation containing &#x1d4b0;. Suppose that G is a group with a normal subgroup H such that G/H ∈ ℱ. If all maximal subgroups of any Sylow subgroup of F*(H) are c-normal in G, then G ∈ ℱ. Theorem Let ℱ be a saturated formation containing &#x1d4b0;. Suppose that G is a group with a normal subgroup H such that G/H ∈ ℱ. If all minimal subgroups and all cyclic subgroups of F*(H) are c-normal in G, then G ∈ ℱ.

On c -Normal Maximal and Minimal Subgroups of Sylow Subgroups of Finite Groups. II

A subgroup H of a finite group G is called c-normal in G if there exists a normal subgroup N of G such that G = HN and $H \cap N \leq H_{G} = {\rm core}_{G}(H)$. In this paper, we investigate the class of groups of which every maximal subgroup of its Sylow p-subgroup is c-normal and the class of groups of which some minimal subgroups of its Sylow p-subgroup is c-normal for some prime number p. Some interesting results are obtained and consequently, many known results related to p-nilpotent groups and p-supersolvable groups are generalized.

On c-normal maximal and minimal subgroups of Sylow p-subgroups of finite groups

A subgroup Hof a finite group Gis said to be c-normal in Gif there exists a normal subgroup Nof Gsuch that HN=Gand H∩ N≤ H G =core G(H).In this paper we shall investigate the influence of c-normality of some subgroups on the strcture of finite groups further, and obtain some results on some kinds of weaker conditions.

The influence of c-normality of subgroups on the structure of finite groups II *

A characterization of the hypercyclically embedded subgroups of finite groups

In this paper, it is proved that the class of all finite supersoluble groups with elementary abelian Sylow subgroups is just the class of all finite groups for which every minimal subgroup is complemented. The structure of a finite group under the assumption that all maximal subgroups (respectively 2-maximal) of any Sylow subgroup are complemented is also analyzed.

On complemented subgroups of finite groups

The influence of c-normality of subgroups on the structure of finite groups

An information system is one of the very important mathematical models in the field of artificial intelligence. The notion of information system's homomorphism as a kind of tools to study the relation between two information systems was introduced by Grzymala-Busse (1986). In this paper, some invariant characteristics of an information system under a homomorphism are discussed.

Invariant characteristics of information systems under some homomorphisms. I

Background This study introduces an alternative palliative surgical procedure called laparoscopic bridge choledochoduodenostomy (LBCDD) for patients with advanced malignant obstructive jaundice (AMOJ). Methods Patients with AMOJ who had LBCDD between January 2017 and August 2021 were identified from databases of two institutions in China. Results A total of 35 patients (male 12; female 23) with an average age of 64 years were enrolled. The average diameter of the tumor is 4.24 cm. All patients undertook LBCDD within an average operation time of 75 min with a mean blood loss of 32 ml. One patient had controlled bile leakage after the operation and two developed surgical site infection involving the epigastric orifices. All of them were solved by conservative treatment. All patients were discharged smoothly after an average hospital stay of 5.5 days, and no conversion to open surgery was required. Conclusions LBCDD is a safe and efficient palliative surgery, which has a good therapeutic effect on patients with AMOJ.

/pdf/an-alternative-palliative-surgical-method-for-advanced-248o5keb.pdf

An alternative palliative surgical method for advanced malignant obstructive jaundice: Laparoscopic bridge choledochoduodenostomy

Invariant characters of information systems under some homomorphisms

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