The Divisibility Problem for subsemigroups of Lie groups

Some finite groups with divisibility graph containing no triangles

Let $G$ be a finite group. The graph $D(G)$ is a divisibility graph of $G$. Its vertex set is the non-central conjugacy class sizes of $G$ and there is an edge between vertices $a$ and $b$ if and only if $a|b$ or $b|a$. In this paper, we investigate the structure of the divisibility graph $D(G)$ for a non-solvable group with $sigma^{ast}(G)=2$, a finite simple group $G$ that satisfies the one-p...

On the Embedding Problem for Infinitely Divisible Distributions on Certain Lie Groups with Toral Center

non-divisibility for abelian groups

Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting   all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...

Historical Links to a Lie Theory of Semigroups

In the past fteen years there has emerged a substantial body of mathematics that one might appropriately refer to as a Lie theory of semigroups. In the narrowest sense, such a theory is concerned with the structure of subsemigroups of Lie groups, particularly those subsemigroups that are in an appropriate sense \innnitesimally generated," that is, are determined by a subtangent object in the Li...

Bounds for the dimension of the $c$-nilpotent multiplier of a pair of Lie algebras

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.