let $g$ be a finite group and $pi_{e}(g)$ be the set of element orders of $g $. let $k in pi_{e}(g)$ and $s_{k}$ be the number of elements of order $k $ in $g$. set nse($g$):=${ s_{k} | k in pi_{e}(g)}$. in this paper, it is proved if $|g|=|$ pgl$_{2}(q)|$, where $q$ is odd prime power and nse$(g)= $nse$($pgl$_{2}(q))$, then $g cong $pgl$_

Canonical orders, introduced in the minimal model program for orders [CI05], are simultaneous generalisations of Kleinian singularities k[[s, t]], G < SL2 and their associated skew group rings k[[s, t]]∗G. In this paper, we construct minimal resolutions of canonical orders via non-commutative cyclic covers and skew group rings. This allows us to exhibit a derived equivalence between minimal res...

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm $T$. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained fr...

Abstract We explore the relationship between weighted path orders and (monotonic) semantic orders. Our findings reveal that can be considered instances of a variant comprise order pairs. This observation leads to generalization does not impose simplicity on their underlying algebras. As result, generalized version is capable proving termination term rewrite systems beyond realm simple terminati...

Objectives To assess the extent to which funding and study design are associated with high reprint orders. Design Case-control study. Setting Top articles by size of reprint orders in seven journals, 2002-09. Participants Lancet, Lancet Neurology, Lancet Oncology (Lancet Group), BMJ, Gut, Heart, and Journal of Neurology, Neurosurgery & Psychiatry (BMJ Group) matched to contemporaneous articles ...