Some remarks on Lorenzen $r$-group of partly ordered groups

Some remarks on the group of R - equivalenceclasses of semisimple groups over arithmetic

We compute the group of R-equivalence classes of some simple simply connected algebraic groups of types 3;6 D 4 and E 6 deened over an algebraic number eld. It is also proved that the variety of a semisim-ple algebraic group G deened over a p-adic eld K is rational over K if all its absolutely simple components are deened over K and have a type diierent from A n ; 2 D n ; in particular, the cor...

Some Remarks on Commuting Fixed Point Free Automorphisms of Groups

In this a‌r‌t‌i‌c‌l‌e we will find n‌e‌c‌e‌s‌s‌a‌r‌y and s‌u‌f‌f‌i‌c‌i‌e‌n‌t c‌o‌n‌d‌i‌t‌i‌o‌n‌s for a f‌i‌x‌e‌d  p‌o‌i‌n‌t f‌r‌e‌e autom‌o‌r‌p‌h‌i‌s‌m (f‌p‌f a‌u‌t‌o‌m‌o‌r‌p‌h‌i‌s‌m) o‌f a g‌r‌o‌u‌p t‌o b‌e a c‌o‌m‌m‌u‌t‌i‌n‌g a‌u‌t‌o‌m‌o‌r‌p‌h‌i‌s‌m. F‌o‌r a given prim‌e ‌ we  f‌i‌n‌d t‌h‌e s‌m‌a‌l‌l‌e‌s‌t o‌r‌d‌e‌r o‌f a n‌o‌n a‌b‌e‌l‌i‌a‌n p-g‌r‌o‌u‌p a‌d‌m‌i‌t‌t‌i‌n‌g a c‌o‌m‌m‌u‌t‌i‌n‌g f...

Compatible elements in partly ordered groups

Some conditions equivalent to a strong quasi-divisor property (SQDP) for a partly ordered group G are derived. It is proved that if G is defined by a family of t-valuations of finite character, then G admits an SQDP if and only if it admits a quasi-divisor property and any finitely generated t-ideal is generated by two elements. A topological density condition in topological group of finitely g...

On Partly Ordered Fields

Some Remarks on Subgroups of Hyperbolic Groups

If G is a hyperbolic group, where G = H oφ Z, H is finitely presented, and φ is an automorphism of H, then H satisfies a polynomial isoperimetric inequality. Necessary and sufficient conditions of homological character are given for a finitely presented subgroup H of a hyperbolic group to be hyperbolic (resp. a quasi-convex subgroup). If Y is a connected subcomplex of the finite connected 2comp...