In this paper we prove the following theorem. Let S be a linear space. Assume that S has an automorphism group G which is line-transitive and point-imprimitive with k < 9. Then S is one of the following:(a) A projective plane of order 4 or 7, (a) One of 2 linear spaces with v = 91 and k = 6, (b) One of 467 linear spaces with v = 729 and k = 8. In all cases the full automorphism group Aut(S) is ...

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

Based on an extremely simple program notation more advanced program features can be developed in linear projective program syntax such as conditional statements, while loops, recursion, use of an evaluation stack, object classes, method calls etc. Taking care of a cumulative and bottom up introduction of such complex features while providing appropriate projections into the lower levels of lang...

We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more stringent criterion of nonexponential growth of the degrees of the iterates. We show that the linearisable mappings are characterised by a very special degree grow...

Let G be a finite group. The character degree graph [Formula: see text] of G is the graph whose vertices are the prime divisors of character degrees of G and two vertices p and q are joined by an edge if pq divides the character degree of G. Let [Formula: see text] be the projective special linear group of degree n over a finite field of order q. Khosravi et. al. have shown that the simple grou...

Let G be a non-abelian group. The non-commuting graph AG of G is defined as the graph whose vertex set is the non-central elements of G and two vertices are joint if and only if they do not commute. In a finite simple graph Γ, the maximum size of complete subgraphs of Γ is called the clique number of Γ and denoted by ω(Γ). In this paper, we characterize all non-solvable groups G with ω(AG) ≤ 57...

Let X be a smooth projective variety defined over an algebraically closed field, and let L be an ample line bundle over X . We prove that for any smooth hypersurface D on X in the complete linear system |L|, the inclusion map D →֒ X induces an isomorphism of fundamental group schemes, provided d is sufficiently large and dimX ≥ 3. If dimX = 2, and d is sufficiently large, then the induced homomo...

DRAFT VERSION The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor representations of the Rotation and Lorentz groups are irreducible. The spinor fields are space-time dependent spinors, solutions of the free Dirac equation. We define the Majorana-Fourier transform and relate it to the linear momentum of a spin one-half Poincare group representation. We sh...