Let $G$ be a finite non-abelian $p$-group and $L(G)$ denotes the absolute center of $G$. Also, let $Aut^{L}(G)$ and $Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $Aut_c(G)=Aut^{L}(G)$. We also characterize all finite non-abelian $p$-groups of order $p^...

Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the Frattini subgroup of $G$. It is shown that the nilpotency class of $Autf(G)$, the group of all automorphisms of $G$ centralizing $G/ Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of maximal class. We also determine the nilpotency class of $Autf(G)$ when $G$ is a finite abelian $p$-group.

BACKGROUND Recombinant human B-type natriuretic peptide (rhBNP) has been indicated for the treatment of acute decompensated heart failure (ADHF). However, the therapeutic efficacy of intravenous rhBNP is not always satisfactory in patients with extremely high blood BNP levels. In this study, we evaluated the effects of rhBNP on patients with different BNP levels. METHODS One hundred and five ...

OBJECTIVE One of the critical components in the postoperative care is pain. Given that little research has been done regarding the analgesic effects of intra-articular injection of ketamine, this study was aimed to compare the analgesic effect of intra-articular and extra-articular injection of morphine and ketamine compound in arthrotomy surgery under spinal anesthesia. METHODS A total of 50...

We study conjugacy closed loops (CC-loops) and power-associative CC-loops (PACC-loops). If Q is a PACC-loop with nucleus N , then Q/N is an abelian group of exponent 12; if in addition Q is finite, then |Q| is divisible by 16 or by 27. There are eight nonassociative PACC-loops of order 16, three of which are not extra loops. There are eight nonassociative PACC-loops of order 27, four of which h...

Imaging has always been an integral part of the assessment of SpA. This group of diseases involving the axial skeleton and peripheral joints is a particularly intriguing area for sonographers, because it requires the evaluation of both articular and extra-articular regions. Among extra-articular features enthesitis has recently emerged as an area of special interest for both basic science and c...

Let $G$ be an abelian group with identity $e$. $R$ a $G$-graded commutative ring and $M$ graded $R$-module. In this paper we will obtain some results concerning the generalized 2-absorbing submodules their homogeneous components. Special attention has been paid, when rings are gr-Noetherian, to find extra properties of these submodules.