Критерий флаг-транзитивности проективной линейной группы, определенной над подкольцом основного тела

It is proved that a projective linear group over a subring of a skew field is flag-transitive if and only if the subring is a Bezout domain and its (left and right) fraction sets coincide with the skew field. This result gives answer for Problem 11.70(b) from Kourovka Notebook.