We study finite groups G having a normal subgroup H and \(D \subset \setminus H, D \cap D^{-1}=\emptyset ,\) such that the multiset \(\{ xy^{-1}:x,y \in D\}\) has every non-identity element occur same number of times (such is called DRAD difference set). show there are no order \(4p^2\), where p an odd prime.

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...

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal h $ -subgroup in‎ ‎$g$ if $n_g (h)cap h^gleq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ $mathcal h^ast $-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal h$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎assump...

A finite group is called simple when its only normal subgroups are the trivial subgroup and the whole group. For instance, a finite group of prime size is simple, since it in fact has no non-trivial proper subgroups at all (normal or not). A finite abelian group G not of prime size, is not simple: let p be a prime factor of #G, so G contains a subgroup of order p, which is a normal since G is a...

in this paper, we consider locally graded groups in which every non-permutable subgroup is soluble of bounded derived length.

In this paper, we completely classify all the finite p-groups G such that, for every non-normal cyclic subgroup H of G, the quotient group G/HG is cyclic. Mathematics Subject Classification: 20D15

Valuations on a field K are encoded in the absolute Galois group GK of K: They are in one-to-one correspondence to the conjugacy classes of decomposition subgroups of GK which (apart from few exceptions) can be characterized in group theoretic terms. Roughly speaking decomposition subgroups of GK are maximal subgroups of GK with a Sylow-subgroup containing a non-trivial abelian normal subgroup....

A finite group G is called a B-group if every proper subgroup of G is either normal or abnormal in G. In this paper the authors classify the non-B-groups whose proper subgroups are all B-groups.

Lung cancer is a major cause of morbidity and mortality worldwide, therefore identifying biomarkers for the early detection, grading or postoperative follow-up of lung cancer is of clinical significance. In the present study, expression of lung tissue (t)-CXCL16 and t-CXCR6 was examined in 58 patients with non-small cell lung cancer (NSCLC) using immunohistochemical staining, and serum (s)-CXCL...