suppose that  is a finite group. then the set of all prime divisors of  is denoted by  and the set of element orders of  is denoted by . suppose that . then the number of elements of order  in  is denoted by  and the sizes of the set of elements with the same order is denoted by ; that is, . in this paper, we prove that if  is a group such that , where , then . here  denotes the family of suzuk...

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...

Suppose that  is a finite group. Then the set of all prime divisors of  is denoted by  and the set of element orders of  is denoted by . Suppose that . Then the number of elements of order  in  is denoted by  and the sizes of the set of elements with the same order is denoted by ; that is, . In this paper, we prove that if  is a group such that , where , then . Here  denotes the family of Suzuk...

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...

The paper demonstrates reduced order modeling (ROM) of the strongly coupled system level dynamic analysis of micro electro mechanical systems (MEMS) by lumped finite elements (FE) and substructuring implemented in the ANSYS/Multiphysics program. Index terms Micro Electromechanical Systems (MEMS), Finite elements (FE), Coupled analysis, Reduced order modeling (ROM)