Subgroups of free groups

With each subgroup A of a free group F there is associated a number FA called the quasi-index. It is proved that FA=ªA¦ if ¦FA¦ is finite. Some properties of the quasi-index are also established, in particular that the analog of Lagrange's theorem is valid for it: FB FA AB if A B as well as generalizations of Howson's and Byrnes' theorems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1115–1119, July–August, 1991.