Subgroups in T-groups

A subgroup D of the group G is called polynormal if for it there exists a fan (RZhMat, 1980, 5A208) and all basis subgroups G of this fan are D-complete (i.e., D^G =G). All subgroups in G are polynormal if and only if G is a T-group (the relation of normality for subgroups is transitive).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 103, pp. 62–65, 1980.The authors express gratitude to Z. I. Borevich for posing the problem and interest in the work.