We give two applications of the recent classification of locally finite simple finitary skew linear groups. We show that certain irreducible finitary skew linear groups of infinite dimension, generate the variety of all groups and have infinite Prüfer rank.

We will describe the relationship between indecomposable characters of Fin(N) and its ergodic invariant random subgroups; we interpret each Thoma character ?(?;?) as an asymptotic limit a naturally associated sequence induced from linear Young subgroups finite symmetric groups.

the non-commuting graph $nabla(g)$ of a non-abelian group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we 'll prove that if $g$ is a finite group with $nabla(g)congnabla(bs_{n})$, then $g cong bs_{n}$, where $bs_{n}$ is the symmetric group of degre...

in this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

Abstract In this paper, we discuss the generalization of finitary 2-representation theory 2-categories to birepresentation bicategories. previous papers on subject, classification simple transitive 2-representations a given 2-category was reduced that for certain subquotients. These reduction results were all formulated as bijections between equivalence classes 2-representations. generalize the...