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...

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...

Using the Luthar–Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle’s conjecture on prime graphs.

One of the important problems in group theory is characterization of a group by a given property, that is, to prove there exist only one group with a given property. Let  be a finite group. We denote by  the largest order of elements of . In this paper, we prove that some Suzuki groups are characterizable by order and the largest order of elements. In fact, we prove that if  is a group with  an...

Donor-acceptor type light-harvesting molecular wires are covalently attached to a borondoped diamond surface via a combination of diazonium electrografting and Suzuki crosscoupling. For the Suzuki reaction, various catalytic systems are compared with respect to their imposed surface coverage. Combining 2-dicyclohexylphosphino-2’,6’-dimethoxybiphenyl (SPhos) and Pd(0), the diamond coverage impro...

It is shown that if a spread of a finite split Cayley hexagon is translation with respect to two disjoint flags then it is either a hermitian spread or a Ree–Tits spread. Analogously, if an ovoid of a classical generalized quadrangle Qð4; qÞ is translation with respect to two disjoint flags then it is either an elliptic quadric or a Suzuki–Tits ovoid. In the course of obtaining these results, w...

* This investigation is supported by the National Science Foundation G. 9654. 1 Brauer, R., and M. Suzuki, "On Finite Groups of Even Order Whose 2-Sylow Group is a Quaternion Group," these PROCEEDINGS, 45, 1757-1759 (1959). 2 Feit, W., "On Groups Which Contain Frobenius Groups as Subgroups," Proc. Symp. Pure Math., 1, 22-28 (1959). 3 Feit, W., M. Hall, and J. Thompson, "Finite Groups in Which t...

In this paper we consider the Suzuki curve y + y = x0(x + x) over the field with q = 2 elements. The automorphism group of this curve is known to be the Suzuki group Sz(q) with q(q − 1)(q + 1) elements. We construct AG codes over Fq4 from a Sz(q)-invariant divisor D, giving an explicit basis for the Riemann-Roch space L(lD) for 0 < l ≤ q − 1. These codes then have the full Suzuki group Sz(q) as...