Finite -Group with Small Abelian Subgroups

A finite -group is said to have the property , if, for any abelian subgroup of , there is . We show that if satisfies , then has the following two types: (1) is isoclinic to some stem groups of order , which form an isoclinic family. (2) is isoclinic to a special -group of exponent . Elementary structures of groups with are determined.