The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...

Mat r x ( F q ) o f a l l r b y r m a t r i c e s o v e r F q , b y C t h e g r o u p G L t i ( F q ) o f t h e u n i t s of M, and by S the special linear subgroup SL , (F q ) o f C . F o r a n a r b i t r a r y field F containing F q , l e t U s t a n d f o r t h e ( c o m m u t a t i v e ) p o l y n o m i a l a l g e b r a F[xl, , x r ] , a n d c o n s i d e r U g r a d e d a s u s u a l : U...

At the 1988 Oberwolfach Computational Group Theory meeting, Joachim Neubiiser asked for an efficient algorithm to decide whether the subgroup of the general linear group GL(d, q) generated by a given set X of non-singular d X d matrices over a finite field ¥q contains the special linear group SL(rf, q). Amplifying the problem he said he would be happy to have a program that could be used for ge...

In this paper we study characters on special linear groups SLn(R), where R is either an infinite field or the localization of an order in a number field. We give several applications to the theory of measure-preserving actions, operator-algebraic superrigidity, and almost homomorphisms.