‎let $h$ be a prefrattini subgroup of a soluble finite group $g$‎. ‎in the‎ ‎paper it is proved that there exist elements $x,y in g$ such that the equality‎ ‎$h cap h^x cap h^y = phi (g)$ holds‎.

‎In 1970‎, ‎Menegazzo [Gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali‎, ‎ Atti Accad‎. ‎Naz‎. ‎Lincei Rend‎. ‎Cl‎. ‎Sci‎. ‎Fis‎. ‎Mat‎. ‎Natur. 48 (1970)‎, ‎559--562.] gave a complete description of the structure of soluble $IM$-groups‎, ‎i.e.‎, ‎groups in which every subgroup can be obtained as intersection of maximal subgroups‎. ‎A group $G$ is said to have the $FM$...

in this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. after obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. the number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. by exploiting the order, we label the s...

The Hawaiian Drosophilidae contains approximately 1000 species, placed in species groups and subgroups based largely on secondary sexual modifications to wings, forelegs and mouthparts. Members of the spoon tarsus subgroup possess a cup-shaped structure on the foretarsi of males. Eight of the twelve species in this subgroup are found only on the Big Island of Hawaii, suggesting that they have d...

Nucleotide sequences of the spacer region of the histone gene H2A-H2B from 36 species of Drosophila melanogaster species group were determined. The phylogenetic trees were reconstructed with maximum parsimony, maximum likelihood, and Bayesian methods by using Drosophila pseudoobscura as the out group. Our results show that the melanogaster species group clustered in three main lineages: (1). mo...

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ord...

The discovery of (interesting) subgroups has a high practical relevance in all domains of science or business. For example, consider statements such as: ”the unemployment rate is above average for young men with a low educational level”, ”smokers with a positive family history are at a significantly higher risk for coronary heart disease”, or ”single males living in rural areas do rarely take o...

In observational studies, identification of associations within particular subgroups is the usual method of investigation. As an exploratory method, it is the bread and butter of epidemiological research. Nearly everything that has been learned in epidemiology has been derived from the analysis of subgroups. In a randomized clinical trial, the entire purpose is the comparison of the test subjec...

A major obstacle to successful oral vaccination is the lack of antigen delivery systems that are both safe and highly efficient. Conventional replication-incompetent adenoviral vectors, derived from human adenoviruses of subgroup C, are poorly efficient in delivering genetic material to differentiated intestinal epithelia. To date, 51 human adenovirus serotypes have been identified and shown to...