@article{Purkayastha_Goswami_Debnath_2017, title={Characterization of a hyperperfect group}, volume={33}, url={https://matematika.utm.my/index.php/matematika/article/view/861}, DOI={10.11113/matematika.v33.n1.861}, abstractNote={<p>In this work, we have introduced the notion of hyperperfect group. A group of order n is said to be hyperperfect if there exists a natural number k such that n-1 = k[σ(n)-n-1] where σ(n) denotes the sum of positive divisors of n. We have also established a condition under which a cyclic group is hyperperfect. We have established that no group of prime order is hyperperfect and investigated the same for groups of various non-prime order. We have also determined an upper bound of the order of a hyperperfect group.</p>}, number={1}, journal={MATEMATIKA}, author={Purkayastha, Saugata and Goswami, Dr. Jituparna and Debnath, Bhargab}, year={2017}, month={Sep.}, pages={97–103} }