$m$-Wielandt series in infinite groups


In a group $G$, $u_m(G)$ denotes the subgroup of the elements which normalize every {\sn} {\sg} of $G$ with defect at most $m$. The $m$-Wielandt series of $G$ is then defined in a natural way. $G$ is said to have finite $m$-Wielandt length if it coincides with a term of its $m$-Wielandt series. We investigate the structure of infinite groups with finite $m$-Wielandt length.