in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

The loricate choanoflagellate genera Diaphanoeca Ellis and Crinolina Thomsen encompass a total of ten species. majority these are recorded from the warm water regions reported on here. A distinct morphological dichotomy characterizes genus as currently circumscribed. species distribute themselves within ‘D. grandis subgroup’ pedicellata distinguished e.g., position protoplast inside lorica cham...

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

Let G be a nite group and be a set of primes. Put d (G) = k (G)=jGj where k (G) is the number of conjugacy classes of -elements in G and jGj is the -part of the order of G. In this paper we initiate the study of this invariant by showing that if d (G) > 5=8 then G possesses an abelian Hall -subgroup, all Hall -subgroups of G are conjugate, and every -subgroup of G lies in some Hall -subgroup of...

background: sulfur mustard (sm) is an alkylating agent that has been used as a chemical warfare gas during world war ii and by iraqi army in the iran-iraq conflict between 1983 and 1988. sm can cause serious organ damages especially ocular, neurologic, coetaneous, bone marrow and pulmonary complications. on the other hand dexmedetomidine is a α2 agonist with sedative and analgesic effect with a...

A subgroup H of G = (Z/dZ)× is called balanced if every coset of H is evenly distributed between the lower and upper halves of G, i.e., has equal numbers of elements with representatives in (0, d/2) and (d/2, d). This notion has applications to ranks of elliptic curves. We give a simple criterion in terms of characters for a subgroup H to be balanced, and for a fixed integer p, we study the dis...

The sequence/function space in the D-mannonate dehydratase subgroup (ManD) of the enolase superfamily was investigated to determine how enzymatic function diverges as sequence identity decreases [Wichelecki, D. J., et al. (2014) Biochemistry 53, 2722-2731]. That study revealed that members of the ManD subgroup vary in substrate specificity and catalytic efficiency: high-efficiency (kcat/KM = 10...

Introduction. If d is a positive square-free integer let Id be the ring of integers in Q(\Jd). Id is a Euclidean domain if d = 1, 2, 3, 7, 11. The groups PSL2(/d) = Fd over these Euclidean rings have recently been investigated. Methods for generating presentations as well as actual presentations were given in [2], [3] and [8], while these groups were shown to be describable in terms of generali...

Rheumatoid arthritis (RA) is an autoimmune disease that is characterized by chronic inflammation affecting target tissues including the joints, bones, and synovial membrane. However, the etiology and pathogenesis of RA remains to be determined, and investigations into the treatment of RA are imperative. Vitamin D (Vit D) was previously found to be associated with the activity of RA and exerts t...

Abstract We prove that there exists a universal constant D such if p is prime divisor of the index Fitting subgroup finite group G , then number conjugacy classes at least $Dp/\log_2p$ . conjecture we can take $D=1$ and for solvable groups, $D=1/3$