On groups with two isomorphism classes of central factors

The structure of groups which have at most two isomorphism classes of central factors ($B_۲$-groups) are investigated‎. ‎A complete description of $B_۲$-groups is obtained in the locally finite case and in the nilpotent case‎. ‎In addition detailed information is obtained about soluble $B_۲$-groups‎. ‎Also structural information about insoluble $B_۲$-groups is given‎, ‎in particular when such a group has the derived subgroup satisfying the minimal condition‎.

Keywords:

‎Center‎ , ‎Isomorphism types‎ , ‎locally finite groups‎ , ‎locally graded groups