In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...

s of lectures for Banff meeting, Groups and Geometries, May 4-8, 2015 Michael Aschbacher: Quaternion fusion packets Abstract I’ll discuss work on a fusion theoretic version of the so-called Classical Involution Theorem for groups. The project is part of a program to simplify part of the proof of the theorem classifying the finite simple groups.I’ll discuss work on a fusion theoretic version of ...

A group is called extended residually finite (ERF) if every subgroup is closed in the profinite topology. The ERF-property is studied for nilpotent groups, soluble groups, locally finite groups and FC-groups. A complete characterization is given of FC-groups which are ERF. 2000 Mathematics Subject Classification: Primary 20E26.

a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

a group $g$ is said to be a c-tidy group if for every element $x in g setminus k(g)$‎, ‎the set $cyc(x)=lbrace y in g mid langle x‎, ‎y rangle ; {rm is ; cyclic} rbrace$ is a cyclic subgroup of $g$‎, ‎where $k(g)=underset{x in g}bigcap cyc(x)$‎. ‎in this short note we determine the structure of finite c-tidy groups‎.

fuzzy groups and fuzzy theory have a lot of applications in several sciences such as mathematics, computer science, computer and electrical engineering. hence, counting the number of fuzzy subgroups of finite groups to classify them is an important issue in fuzzy theory. the main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group g z p1 ...