this thesis basically deals with the well-known notion of the bear-invariant of groups, which is the generalization of the schur multiplier of groups. in chapter two, section 2.1, we present an explicit formula for the bear-invariant of a direct product of cyclic groups with respect to nc, c>1. also in section 2.2, we caculate the baer-invatiant of a nilpotent product of cyclic groups wuth resp...

‎In this paper‎, ‎a new estimate of exponential type of auxiliary information to help simple random sampling without replacement of the finite population mean is introduced‎. ‎This new estimator with a few other estimates using two real data sets are compared with the mean square error‎.