On Several Classes of Simple Groups

Quantum conjugacy classes of simple matrix groups

Let G be a simple complex classical group and g its Lie algebra. Let U~(g) be the Drinfeld-Jimbo quantization of the universal enveloping algebra U(g). We construct an explicit U~(g)-equivariant quantization of conjugacy classes of G with Levi subgroups as the stabilizers.

On several classes of monographs

Some numerical results on two classes of finite groups

In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$K(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. Also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...

Products of Conjugacy Classes in Finite and Algebraic Simple Groups

We prove the Arad–Herzog conjecture for various families of finite simple groups — if A and B are nontrivial conjugacy classes, then AB is not a conjugacy class. We also prove that if G is a finite simple group of Lie type and A and B are nontrivial conjugacy classes, either both semisimple or both unipotent, then AB is not a conjugacy class. We also prove a strong version of the Arad–Herzog co...

On Subjunctive Classes of Groups