‎In this study‎, ‎Frattini supplement subgroup and Frattini supplemented group‎ ‎are defined by Frattini subgroup‎. ‎By these definitions‎, ‎it's shown that‎ ‎finite abelian groups are Frattini supplemented and every conjugate of a‎ ‎Frattini supplement of a subgroup is also a Frattini supplement‎. ‎A group action‎ ‎of a group is defined over the set of Frattini supplements of a normal‎ ‎subgro...

AIMS A causal relationship between vitamin D deficiency and the incidence of diabetes mellitus has been suggested, but little research has been conducted on the Korean population. METHODS We analysed the glucose tolerance status and serum 25-hydroxyvitamin D concentrations in 12263 subjects >19 years old who were registered for the Korea National Health and Nutrition Examination Survey, 2008-...

We are concerned with torsion subgroups of Lie groups. We extend the classical result of C. Jordan on the structure of finite linear groups to torsion subgroups of connected Lie groups. 1. In [1], Boothby and Wang proved that, for any connected Lie group G, there exists a number k{G) such that any finite subgroup contains an abelian normal subgroup whose index is bounded by k{G), thereby genera...

In this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. We establish the orthogonality relations fo...

‎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 $fm$...

We obtain a strong law of large numbers and a functional central limit theorem, as t → ∞, for the number of records up to time t and the Lebesgue measure (length) of the subset of the time interval [0, t] during which the Poisson process is in a record lifetime. strong law of large numbers.

‎In the classical group theory there is‎ an open question‎: ‎Is every torsion free n-Engel group (for n ≥ 4)‎, nilpotent?‎. ‎To answer the question‎, ‎Traustason‎ [11] showed that with some additional conditions all‎ ‎4-Engel groups are locally nilpotent‎. ‎Here‎, ‎we gave some partial‎ answer to this question on Engel fuzzy subgroups‎. ‎We show that if μ is a normal 4-Engel fuzzy‎ subgroup of ...

Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the influence of minimal S-embedded subgroups on the structure of finite groups. We determine the structure the finite grou...

Let G be a finite primitive group such that there is only one minimal normal subgroup M in G, this M is nonabelian and nonsimple, and a maximal normal subgroup of M is regular. Further, let H be a point stabilizer in G. Then H (1 M is a (nonabelian simple) common complement in M to all the maximal normal subgroups of M, and there is a natural identification ofMwith a direct power T m of a nonab...

BACKGROUND Despite extensive research, the pathogenesis of polycystic ovary syndrome (PCOS) remains unclear. Putatively, an elevated circulating concentration of insulin inhibits the production of insulin-like growth factor binding protein-1 (IGFBP-1), thus increasing the level of free IGF-I in serum and stimulating ovarian androgen production. Decreased IGFBP-1 has been reported in PCOS and in...