Let G be a transitive permutation group on a set ? and let m be a positive integer. If no element of G moves any subset of ? by more than m points, then |? | [2mp I (p-1)] wherep is the least odd primedividing |G |. When the bound is attained, we show that | ? | = 2 p q ….. q where ? is a non-negative integer with 2 < p, r 1 and q is a prime satisfying p < q < 2p, ? = 0 or 1, I i n....

let g be a transitive permutation group on a set ? and let m be a positive integer. if no element of g moves any subset of ? by more than m points, then |? | [2mp i (p-1)] wherep is the least odd primedividing |g |. when the bound is attained, we show that | ? | = 2 p q ….. q where ? is a non-negative integer with 2 < p, r 1 and q is a prime satisfying p < q < 2p, ? = 0 or 1, i i n. furthermore...

We introduce several q-differential equations of higher order which are related to q-Bernoulli polynomials and obtain a symmetric property in this paper. By giving q-varying variations, we identify the shape approximate roots polynomials, solution order, find conjectures associated with them. Furthermore, based on create Mandelbrot set Julia variety figures.

Abstract In the present investigation, with help of certain higher-order q -derivatives, some new subclasses multivalent -starlike functions which are associated Janowski defined. Then, interesting results, for example, radius problems and results related to distortion, derived. We also derive a sufficient condition coefficient inequalities our defined function classes. Some known consequences ...

let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

Let $G$ be a finite group. We construct the prime graph of $ G $,which is denoted by $ Gamma(G) $ as follows: the vertex set of thisgraph is the prime divisors of $ |G| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ G $ contains anelement of order $ pq $.In this paper, we determine finite groups $ G $ with $ Gamma(G) =Gamma(L_3(q)) $, $2 leq q < 100 $ and prov...