On groups with two isomorphism classes of central factors

The structure of groups which have at most two isomorphism classes of central factors (B2-groups) are investigated‎. ‎A complete description of B2-groups is obtained in the locally finite case and in the nilpotent case‎. ‎In addition detailed information is obtained about soluble B2-groups‎. ‎Also structural information about insoluble B2-groups is given‎, ‎in particular when such a group has the derived subgroup satisfying the minimal condition‎.