On solutions of “equations in symmetric groups”

On monochromatic solutions of equations in groups

We show that the number of monochromatic solutions of the equation x1 1 x α2 2 · · ·xαr r = g in a 2-coloring of a finite group G, where α1, . . . ,αr are permutations and g ∈ G, depends only on the cardinalities of the chromatic classes but not on their distribution. We give some applications to arithmetic Ramsey statements.

On the Parameterization of solutions for equations in Free Groups

Plane Symmetric Solutions of Gravitational Field Equations in Five Dimensions

We present the effective field equations obtained from a generalized gravity action with Euler-Poincaré term and a cosmological constant in a D dimensional bulk space-time. A class of plane-symmetric solutions that describe a 3-brane world embedded in a D = 5 dimensional bulk space-time are given. Paper presented at the 5th Workshop on Quantization, Dualities and Integrable Systems, Pamukkale U...

the impact of e-readiness on ec success in public sector in iran the impact of e-readiness on ec success in public sector in iran

acknowledge the importance of e-commerce to their countries and to survival of their businesses and in creating and encouraging an atmosphere for the wide adoption and success of e-commerce in the long term. the investment for implementing e-commerce in the public sector is one of the areas which is focused in government‘s action plan for cross-disciplinary it development and e-readiness in go...

A NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS

The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.