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96.949  Articles
1 of 9.696 pages  |  10  records  |  more records»
Let GG be a finite additive abelian group with exponent n>1n>1, and let a1,…,an-1a_1,\ldots,a_{n-1} be elements of GG. We show that there is a permutation s?Sn-1\sigma\in S_{n-1} such that all the elements sas(s) (s=1,…,n-1)sa_{\sigma(s)}\ (s... see more

Let G be a subgroup of Sn. For x ? G, the index of x in G is denoted by ind x is the minimal number of 2-cycles needed to express x as a product. In this paper, we define a new kind of graph on G, namely the index graph and denoted by Gind(G). Its vertex ... see more

This report is essentially an upgrade of the results of Audu (see [1] and [2]) on some finite permutation groups. It consists of the basic procedure for computing wreath product of groups. We also discussed the conditions under which the wreath products o... see more

Let G be a subgroup of the symmetric group Sn. Then G has the Erdos-Ko-Rado (EKR) property, if the size of any intersecting subset of G is bounded above by the size of a point stabilizer of G. The aim of this paper is to investigate the EKR and the strict... see more

We develop a new framework for analysing finite connected, oriented graphs of valency four, which admit a vertex-transitive and edge-transitive group of automorphisms preserving the edge orientation. We identify a sub-family of `basic' graphs such that ea... see more

The random permutation is the Fraïssé limit of the class of finite structures with two linear orders. Answering a problem stated by Peter Cameron in 2002, we use a recent Ramsey-theoretic technique to show that there exist precisely 39 closed supergroups ... see more

A rainbow path in an edge-colored graph G is a path that every two edges have different colors. The minimum number of colors needed to color the edges of G such that every two distinct vertices are connected by a rainbow path is called... see more

Suppose G is with finite torsion-free rank a coproduct of p-mixed countable abelian groups and F is a field with characteristic p such that the group algebras FG and FH are F -isomorphic for another group H . Then G and H are isomorphic.

The aim of this paper is to give a detailed account of a problema posed by P. Lescot regarding asymptotic commutativity degree of finite groups.

1 of 9.696 pages  |  10  records  |  more records»