Groups of breadth four have class five

A class of cyclic codes whose duals have five zeros

In this paper, a family of cyclic codes over Fp whose duals have five zeros is presented, where p is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.

Finite groups have even more centralizers

For a finite group $G$‎, ‎let $Cent(G)$ denote the set of centralizers of single elements of $G$‎. ‎In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent‎, ‎then $Gcong S_3‎, ‎D_{10}$ or $S_3times S_3$‎. ‎This result gives a partial and positive answer to a conjecture raised by A‎. ‎R‎. ‎Ashrafi [On finite groups with a given number of centralizers‎, ‎Algebra‎ ‎Collo...

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

A Fractal Non-Contracting Class of Automata Groups

Finite P-groups of Class 2 Have Noninner Automorphisms of Order P

We prove that for any prime number p, every finite non-abelian p-group G of class 2 has a noninner automorphism of order p leaving either the Frattini subgroup Φ(G) or Ω1(Z(G)) elementwise fixed.