We give a simple proof of the result of Grable on the asymptotics of the number of partial Steiner systems S(t,k,m). # 2000 John Wiley & Sons, Inc.J Combin Designs 8:347±352, 2000 Keywords: partical Steiner system; matching; hypergraph 1. INTRODUCTION A partial Steiner system S…t; k;m† is a collection of k-subsets of an m-element set M such that each t-subset is contained in at most one k-subse...

Given a non-decreasing function $$f:\mathbb {N}\rightarrow \mathbb {N}$$ we define single player game on (infinite) connected graphs that call fire retaining. If graph G admits winning strategy for any initial configuration (initial fire) then say has the f-retaining property; in this case if f is polynomial of degree d, retaining property d. We prove having d quasi-isometry invariant class uni...

If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X stabilized by G, then under the assumption that D is nonspecial, we compute a simplified formula for the trace of the natural representation of G on Riemann-Roch space L(D).

It is conjectured that for fixed A, r ≥ 1, and d ≥ 1, there is a uniform bound on the size of the torsion submodule of a Drinfeld A-module of rank r over a degree d extension L of the fraction field K of A. We verify the conjecture for r = 1, and more generally for Drinfeld modules having potential good reduction at some prime above a specified prime of K. Moreover, we show that within an L-iso...

It is known that, if G is a triply transitive permutation group on a finite set X with a regular normal subgroup N, then |N| = 2 (d ̂ 2) or |N| = 3. (See [12; Theorem 11.3].) If N is a regular normal subgroup of a permutation group G on X, xeX, and Gx is the stabiliser of x, then Gx £ G/JV (as abstract group), and so G has a representation on a set Y such that, for xeX, the representations of Gx...

Introduction: Indomethacin increases generation of mitochondrial reactive oxygen species (ROS) which have a crucial role in the indomethacin-induced gastric ulcer. Coenzyme Q10 has an antioxidant activity on mitochondria and cell membranes and protects lipids from oxidation and is essential for stabilizing biological membranes. Superoxide dismutase (SOD) acts as one of the defense mechanisms ag...

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...

in this paper, we will give necessary and sufficient conditions for certain hnnextensions of subgroup separable groups with normal associated subgroup to be conjugacyseparable. in fact, we will show that these hnn extensions are conjugacy separable if and onlyif the normalizer of one of its associated subgroup is conjugacy separable.

let $g$ be a finite group with the identity $e$‎. ‎the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$‎, ‎where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$‎. ‎in th...

Conjecture 1 (A. Potapchik and A. Rapinchuk). Let D be a finite dimensional division algebra over an arbitrary field. Then D# does not have any normal subgroup N such that D#/N is a nonabelian finite simple group. Of course D# is the multiplicative group of D. Conjecture 1 appears in [4]. It is related to the following conjecture of G. Margulis and V. Platonov (Conjectures 9.1 and 9.2, pages 51...