TY - JOUR
AU - Purkayastha, Saugata
AU - Goswami, Dr. Jituparna
AU - Debnath, Bhargab
PY - 2017/09/20
Y2 - 2024/08/04
TI - Characterization of a hyperperfect group
JF - MATEMATIKA
JA - MATEMATIKA
VL - 33
IS - 1
SE - Articles
DO - 10.11113/matematika.v33.n1.861
UR - https://matematika.utm.my/index.php/matematika/article/view/861
SP - 97-103
AB - <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>
ER -