The minimal radical and weakly irreducible groups

Under certain restrictions on a class of groups $\mathfrak M$, closed with respect to epimorphisms, we prove the theorem: a nonunit group contains no accessible $\mathfrak M$-subgroups except the unit group if and only if it is approximated by weakly irreducible (after Birkhoff) groups which contain no nonunit accessible $\mathfrak M$-subgroups.