Dimension subgroups and group homologies

Roman Mikhailov of the Steklov Institute in Moscow

(Joint work with I.B.S. Passi) We consider some conditions on group homologies, which implie dimension property. Also we generalize dimension conjecture for all ideals in the group rings. For example, we consider the transfinite dimension subgroups and show that the (\omega+1)-th dimension subgroup is trivial for any torsion nilpotent group. This problems we consider also over rational numbers. We prove that the dimension series are equal to the transfinite lower central series over the second limit ordinal number over rationals.