‎For a finite group $G$‎, ‎let $nse(G)={m_kmid kinpi_e(G)}$‎, ‎where $m_k$ is the number of elements of order $k$ in $G$‎ ‎and $pi_{e}(G)$ is the set of element orders of $G$‎. ‎In this paper‎, ‎we prove that $Gcong L_m(2)$ if and only if $pmid |G|$ and $nse(G)=nse(L_m(2))$‎, ‎where $min {n,n+1}$ and $2^n-1=p$ is a prime number.

The restrictions of irreducible modules special linear and symplectic groups in an odd characteristic p with p-large highest weights to a subsystem subgroup H maximal rank two simple components H1 H2 are considered. lower estimate for the number composition factors such restrictions, which not too small H2, is found. estimates Jordan blocks size images certain unipotent elements corresponding r...

Let F be any field of prime characteristic p and let q a power p. We assume that contains the finite order q. A q-polynomial L over is an element polynomial ring F[x] with property all exponents are coefficient x term nonzero. investigate Galois group G F, under assumption L(x)/x irreducible in F[x]. It well known if has q-degree n, its roots n-dimensional vector space acts linearly on this spa...