Several decades ago, John McKay suggested a correspondence between nodes of the affine E8 Dynkin diagram and certain conjugacy classes in the Monster group. Thanks to Monstrous Moonshine, this correspondence can be recast as an assignment of discrete subgroups of PSL2(R) to nodes of the affine E8 Dynkin diagram. The purpose of this article is to give an explanation for this latter correspondenc...

In this paper we classify all finite solvable groups satisfying the following property P5: their orders of representatives are set-wise relatively prime for any 5 distinct non-central conjugacy classes.

We describe all left braces of size 8p for an odd prime p?3,7 and validate the number given by Bardakov, Neschadim Yadav in [2]. give a characterization isomorphism classes semidirect product then description is done first describing 8, as conjugacy regular subgroups corresponding holomorph, checking how many non isomorphic are obtained from each one them.

Let G be a finite group and C(G) be the family of representative conjugacy classes of subgroups of G. The matrix whose H;K-entry is the number of fixed points of the set G=K under the action of H is called the table of marks of G where H;K run through all elements in C(G). In this paper, we compute the table of marks and the markaracter table of groups of order pqr where p, q, r are prime numbers.

Abstract A group G is said to be an FC -group if every conjugacy class of has finite order and a T subnormal subgroup normal in . In this paper we give characterization groups that are both -groups go further the study with few non-normal subgroups sense chain conditions. The structure satisfying maximal, minimal double condition on will described.

‎there are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{z}_{2}$ or $mathbb{z}_{15}$. still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of sylow $p$-subgroups for each prime $p$, etc. in this...

In this survey paper we bring together a number of results concerning to the poset of conjugacy classes of subgroups of some groups. MSC (2000): Primary 20E45, Secondary 20D30, 20E15.