Lagrange’s theorem tells us that if G is a finite group and H ≤ G, then #(H) divides #(G). As we have seen, the converse to Lagrange’s theorem is false in general: if G is a finite group of order n and d divides n, then there need not exist a subgroup of G whose order is d. The Sylow theorems say that such a subgroup exists in one special but very important case: when d is the largest power of ...

This is the latest part of an ongoing project aimed at extending algebraic properties of the classical modular group SL2(Z) to equivalent groups in the theory of Drinfeld modules. We are especially interested in those properties which are important in the classical theory of modular forms. Our results are intended to be applicable to the theory of Drinfeld modular curves and forms. Here we are ...

The continued increase in the size of the protein sequence databases as a result of advances in genome sequencing technology is overwhelming the ability to perform experimental characterization of function. Consequently, functions are assigned to the vast majority of proteins via automated, homology-based methods, with the result that as many as 50% are incorrectly annotated or unannotated ( Sc...

Abstract A subgroup functor τ \tau is said Φ \Phi -regular if for all primitive groups G G , whenever H ∈ ( ) H\in \left(G) a p p -subgroup and N N minimal normal of then <m:mo...

Increased abundance of Gardnerella vaginalis and sialidase activity in vaginal fluid is associated with bacterial vaginosis (BV), a common but poorly understood clinical entity associated with poor reproductive health outcomes. Since most women are colonized with G. vaginalis, its status as a normal member of the vaginal microbiota or pathogen causing BV remains controversial, and numerous clas...

We performed genetic analysis of hybrid sterility and of one morphological difference (sex-comb tooth number) on D. yakuba and D. santomea, the former species widespread in Africa and the latter endemic to the oceanic island of São Tomé, on which there is a hybrid zone. The sterility of hybrid males is due to at least three genes on the X chromosome and at least one on the Y, with the cytoplasm...

Magnus’ Freiheitssatz [20] states that if a group is defined by presentation with m generators and single cyclically reduced relator, this relator contains the last generating letter, then first $$m-1$$ letters freely generate free subgroup. We study an analogue of theorem in Gromov density model random groups [14], showing phase transition phenomenon at $$d_r = \min \{\frac{1}{2}, 1-\log _{2m-...

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-...

(i) A subgroup of PFL(d, q) containing PSL(d, q), in its usual 2-transitive representation; (ii) A collineation group of AG(d, q), containing the group ASL(d, q) of collineations generated by elations, in its usual 2-transitive representation on AG(d, q); (iii) A 7 in its 2-transitive representation of degree 15; (iv) There is a regular normal subgroup, and if x~S then F x acts on S { x } as th...