in this paper we illustrate recent results about factorizations of finite groups into conjugate subgroups. the illustrated results are joint works with john cannon, dan levy, attila mar'oti and iulian i. simion.

This is the latest part of an ongoing project aimed at extending algebraic properties of the classical modular group SL2(Z) to equivalent groups in the theory of Drinfeld modules. We are especially interested in those properties which are important in the classical theory of modular forms. Our results are intended to be applicable to the theory of Drinfeld modular curves and forms. Here we are ...

we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.‎

This paper gives polynomial time quantum algorithms for computing the ideal class group (CGP) under the Generalized Riemann Hypothesis and solving the principal ideal problem (PIP) in number fields of arbitrary degree. These are are fundamental problems in number theory and they are connected to many unproven conjectures in both analytic and algebraic number theory. Previously the best known al...

Background: Cucumber mosaic virus (CMV) from the Bromoviridae family, is one of the most widespread plant viruses in the world. Objectives: In the present study tomato fields in Guilan, Isfahan, Khorasan Razavi, Khuzestan and Tehran provinces were surveyed to determine the presence of CMV subgroups during 2011-2012. Materials and Methods: Out of 305 symptomatic leaf samples ...

An ideal triangulation T of a hyperbolic 3-manifold M with one cusp is non-peripheral if no edge of T is homotopic to a curve in the boundary torus of M . For such a triangulation, the gluing and completeness equations can be solved to recover the hyperbolic structure of M . A planar projection of a knot gives four ideal cell decompositions of its complement (minus 2 balls), two of which are id...

-d) u {00} c= CP = dH, and each a ePSL2(0d) determines an edge which is the geodesic in H having endpoints a//? and y/d. The tesselations 5^ and ^ are by regular ideal octahedra and tetrahedra, respectively, and are classical objects; for example, &\ is constructed in [2]. The tesselations «^, by ideal cuboctahedra, and ST-i, by ideal triangular prisms, are implicit in Chapter 6 of [9]; ^ is a ...

Exploiting the analogy between exemplar models and population coding schemes, we characterize, by means of information theoretic tools, the efficiency of a large but finite population of cells coding for a discrete set of categories (e.g. vowels). The optimal code is shown to typically allocate more cells to class boundaries than to regions further apart. We then discuss the predicted perceptua...