Unique, and Necessarily Cyclic, Subgroup of an Arbitrary Order in a Group

چکیده مقاله

In this paper, some equivalent conditions on a finite group G will be given in order the group G to have a unique, and necessarily cyclic, subgroup of order m,  where m is a fixed divisor of |G|. These conditions are about “the number of cyclic subgroups of particular orders” and “the number of elements of particular orders”.