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Let R be a Г-ring, and σ, τ be two automorphisms of R. An additive mapping d from a Γ-ring R into itself is called a (σ,τ)-derivation on R if d(aαb) = d(a)α σ(b) + τ(a)αd(b), holds for all a,b ∈R and α∈Γ. d is called strong commutativity preserving (SCP) on R if [d(a), d(b)]α = [a,b]α(σ,τ) holds for all a,b∈R and α∈Γ. In this paper, we investigate the commutativity of R by the strong commutativity preserving (σ,τ)-derivation d satisfied some properties, when R is prime and semi prime Г-ring.

Let N be a near-ring, and σ be an automorphisms of N. An additive mapping d from a near-ring N into itself is called a reverse σ-derivation on N if d (xy) = d(y) x + σ(y) d(x), holds for all x, y∈ N. In this paper, we shall investigate the commutativity of N by a reverse σ-derivation d satisfied some properties, when N is a prime ring.

Let M be a prime Г-near ring, and let F and G be two generalized Г-derivations of M with associated Г-derivations D 1 and D 2 respectively. In this paper, we shall investigate the commutativity of M by generalized Г-derivations F and G satisfied some properties.

In this paper we find χ-subgroup for the irreducible characters χ of the Special linear group SL(n,q) when n=2,3 ..