We briefly survey on the classification of finite simple groups. A.M.S. Classification: 20D05, 20D06, 20D08, 20-02.

Using classification of finite simple groups, I show that a finite subgroup G of GL(n)(C), where C = the complex numbers, contains a commutative normal subgroup M of index at most (n + 1)!n(alogn+b). Moreover, if G is primitive and does not contain normal subgroups that are direct products of large alternating groups, then the factor (n + 1)! can be dropped. I further show that similar statemen...

This is the third, and last, of a series of papers dealing with oriented regular representations. Here we complete the classification of finite groups that admit an oriented regular representation (or ORR for short), and give a complete answer to a 1980 question of László Babai: “Which [finite] groups admit an oriented graph as a DRR?” It is easy to see and well-understood that generalised dihe...

let $g$ be a finite group with the identity $e$‎. ‎the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$‎, ‎where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$‎. ‎in th...

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 ...