Let N = Ln(q), n ≥ 2, q a prime power, be a projective linear simple group. We classify all Steiner quadruple systems admitting a group G with N ≤ G ≤ Aut(N). In particular, we show that G cannot act as a group of automorphisms on any Steiner quadruple system for n > 2.

The purpose of this note is to exhibit the automorphism group of a projective bundle P(E) over a simplicial toric variety X when the bundle E is a direct sum of equvariant line bundles. This case is important in the study of moduli of complete intersections on toric varieties including projective spaces. The main result is that the automorphism group of P (E) is, up to a finite group, the semi-...

The main goal of this paper is to construct the Berry-Hannay's model of quantum mechanics on a two dimensional symplectic torus. We construct a simultaneous quantization of the algebra of functions and the linear symplectic group G = SL 2 (Z). We obtain the quan-tization via an action of G on the set of equivalence classes of irre-ducible representations of Rieffel's 2-dimensional quantum torus...

There exists just one regular polytope of rank larger than 3 whose full automorphism group is a projective general linear group PGL2(q), for some prime-power q. This polytope is the 4-simplex and the corresponding group is PGL2(5) ∼= S5.

This paper concerns with a product of circles induced by the quaternionic product considered in a projective manner. Several properties of this composition law are derived and on this way we arrive at some special numbers as roots or powers of unit. We extend this product to cycles as oriented circles and to pairs of circles by using the algebra of octonions. Three applications of the given pro...

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the center of such...