(α,γ)-Anti-Multi-Fuzzy Subgroups and Some of Its Properties

Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.

Some Generalized Normal Subgroups and p-nilpotency of Finite Groups

In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.

FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS

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 C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.

SOME SUBGROUPS OF THE EXTENDED HECKE GROUPS H^－（λq）

The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second commutator subgroup H''(γq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups .H(γq) are studied. Also, relations between them are given.

On θ*-completions of F-abnormal Subgroups

Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HGbelongs to F; otherwise H is said to be F-abnormal in G. In this paper, we investigate the structure of a finite group by θ*-completions of F-abnormal subgroups.

The Intersection of a Maximal Intransitive Subgroup with a Maximal Imprimitive Subgroup

In this paper, we investegate the intersection of a maximal intransitive subgroup with a maximal imprimitive subgroup. And, the structure of the second maximal intransitive subgroup of an alternating group is determined.

On the Equal-height Elements of the Fuzzy Subgroups

The properties of the equal height elements of the fuzzy subroups and the classification of groups by its fuzzy subgroups are discussed.

Finite Groups with only S-seminormal or Selfnormal Subgroups

In this note the author studies such a finite group in which each subgroup is either Sseminormal or selfnormal and characterizes this kind of finite groups.Moreover,the main results in[1] and [2] can be obtained by the conclusion in this note.

s-Conditionally Permutable Subgroups and p-Nilpotency of Finite Groups

A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G, on the structure of finite groups. New criteria for a group G being p-nilpotent are obtained.

LF λ-subgroup Generated by LF Subset

In this paper .an important property layer-preserving of LF group and an concept LF λ-subgroup generated by LF subset will be introduced. On the height of LF group theory ,we recognize the concept generated subgroup more clearly.

Finite Groups Whose Some Subgroups Are S-seminormal

A subgroup H is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable groups to a saturated formation containing the class of finite supersolvable groups.

Two Theorems about Nilpotent Subgroup

In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.

Isolation and Identification of a Subgroup A Avian Leukosis Virus from Imported Meat-type Grand-parent Chickens

An exogenous avian leukosis virus (ALV) strain SDAU09C1 was isolated in DF-1 cells from one of 240 imported 1-day-old white meat-type grand parent breeder chicks. Inoculation of SDAU09C1 in ALV-free chickens induced antibody reactions specific to subgroup A or B. But gp85 amino acid sequence comparisons indicated that SDAU09C1 fell into subgroup A; it had homology of 88.8%-90.3% to 6 reference strains of subgroup A, much higher compared to other subgroups including subgroup B. This is the first report for ALV of subgroup A isolated from imported breeders.

ON F-z-SUPPLEMENTED SUBGROUPS OF FINITE GROUPS

A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.

Establishment of an avian leukosis virus subgroup A-resistant cell line

Rapid diagnostic methods for classifying avian leukosis subgroups in the field were needed for routine, large-scale screening. As a first step in method development, we inserted the avian leukosis virus subgroup A （ALV-A） env gene into plasmid pcDNA3.1/Zeo （＋） and used this construct to transfect DF-1 cells. Zeocin-resistant cells were obtained after 2 weeks of zeocin selection. Then, the cells were analyzed using PCR, immunofluorescence, and Western blot for expression of the envA-encoded envelope protein after 30 serial passages. The DF-1/A cell line was completely resistant to 104 TCIDso/0.1 mL （50% tissue culture infective dose）ALV-A and was partially resistant to 10~ TCIDs0/0.1 mL ALV-A viral particles. By comparing the DF-1/A and DF-1 cell lines, an ALV-A isolate was identified using a gag-specific ELISAfor capsid protein p27. Thus, we established a DF-1/A cell line that was resistant to ALV-A infection. This cell line will be useful as a diagnostic tool.

Fully Secure Identity-based Broadcast Encryption in the Subgroups

In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive security) under three static(i.e. non q-based) assumptions. It is worth noting that only recently Waters gives a short ciphertext broadcast encryption system that is even adaptively secure under the simple assumptions. One feature of our methodology is that it is relatively simple to leverage our techniques to get adaptive security.

On s＊-Completions of Maximal Subgroups of Finite Groups

Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.

Spatial Distribution Pattern and Han Subgroup Characteristics of Traditional Villages in Guangdong

A total of 126 traditional villages in Guangdong were selected for research to analyze their spatial distribution pattern, spatial autocorrelation, and Han subgroup characteristics through the spatial analysis with GIS. The results showed that the traditional villages in Guangdong were distributed compactly, which was similar to that in other provinces; on the prefecture-level city scale, they were mainly distributed in Meizhou, Qingyuan, Zhanjiang, and Zhaoqing, showing a central distribution; on the regional scale, they were mainly distributed in northern Guangdong and the Pearl River Delta, indicating an unbalanced distribution; their density of spatial distribution showed a significant difference with a provincial distribution density of 0.59 per thousand km^2 and the highest distribution density of 2.14 per thousand km^2; there were four gathering areas accommodating many traditional villages, namely Meizhou-Chaoshan area, Guangfo-Dongguan area, Leizhou in Zhanjiang, and Lianzhou in Qingyuan; the spatial distribution of traditional villages, which presented a pattern of hot spot—sub-hot spot—sub-cold spot—cold spot, had a significant global spatial autocorrelation, and areas in similar sizes were tending towards gathering; traditional villages in Guangdong belonged to the Cantonese-speaking group and Hakka-speaking group with a density of 0.59 per thousand km^2 and 0.48 per thousand km^2 respectively, and Han subgroup with the highest distribution density was the minority areas of 1.31 per thousand km^2, followed by Shaozhou dialect area with a density of 1.00 per thousand km^2.

Strongly Modular Subgroup in Finite Group

In this peper,strongly Modular subgroups was defined and studied.

An Investigation on the Parabolic Subgroups of the General Linear Groups by Using GAP

A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups. For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.