Let S be a finite nonabelian simple group, and let H be a subgroup of S . In this work, the dominion (in the sense of Isbell) of H in S in Var(S) is determined, generalizing an example of B.H. Neumann. A necessary and sufficient condition for H to be epimorphically embedded in S is obtained. These results are then extended to a variety generated by a family of finite nonabelian simple groups. S...

This paper considers the appearance of almost difference sets in non-abelian groups. While numerous construction methods for these structures are known in abelian groups, little is known about ADSs in the case where the group elements do not commute. This paper presents a construction method for combining abelian difference sets into nonabelian almost difference sets, while also showing that at...

We study in this paper a theory of free anyons associated to free conformal field theories defined on Riemann surfaces with a discrete and nonabelian group of authomorphisms. The particles are exchanged according to a nonabelian statistics, in which the R−matrix satisfy a multiparametric generalization of the usual Yang−Baxter equations. October 1992 1 Work supported by the Consiglio Nazionale ...

Bestvina, Feighn and Handel proved that every subgroup of the outer automorphism group, Out(Fn), free group rank n is either virtually finitely generated abelian or contains a nonabelian group. In this note we consider more general situation Out(G) free-by-finite G. We show translation discrete

let $g$ be a finite group and let $text{cd}(g)$ be the set of all‎ ‎complex irreducible character degrees of $g$‎. ‎b‎. ‎huppert conjectured‎ ‎that if $h$ is a finite nonabelian simple group such that‎ ‎$text{cd}(g) =text{cd}(h)$‎, ‎then $gcong h times a$‎, ‎where $a$ is‎ ‎an abelian group‎. ‎in this paper‎, ‎we verify the conjecture for‎ ‎${f_4(2)}.$‎

We show the existence of several new infinite families polynomially-growing automorphisms free groups whose mapping tori are CAT(0) free-by-cyclic groups. Such thick, and thus not relatively hyperbolic. These first comprising infinitely many examples for each rank nonabelian group; they contrast strongly with Gersten’s example a thick group which cannot be subgroup group.

Serre [5] has recently proved a general theorem about projective modules over commutative rings. This theorem has the following consequence : If 7T is a finite abelian group, any finitely generated projective module over the integral group ring Zir is the direct sum of a free module and an ideal of Zir. The question naturally arises as to whether this result holds for nonabelian groups x. Serre...

We study mixing properties of epimorphisms of a compact connected finite-dimensional abelian group X . In particular, we show that a set F , |F | > dimX , of epimorphisms of X is mixing iff every subset of F of cardinality (dimX)+1 is mixing. We also construct examples of free nonabelian groups of automorphisms of tori which are mixing, but not mixing of order 3, and show that, under some irred...