Locally Finite Groups All of Whose Subgroups are Boundedly Finite over Their Cores

For n a positive integer, a group G is called core‐n if H / H G has order at most n for every subgroup H of G (where H G is the normal core of H , the largest normal subgroup of G contained in H ). It is proved that a locally finite core‐ n group G has an abelian subgroup whose index in G is bounded in terms of n . 1991 Mathematics Subject Classification 20D15, 20D60, 20F30.