Open AccessCharacterization of a hyperperfect group
Author(s) -
Saugata Purkayastha,
Jituparna Goswami,
B. Debnath
Publication year - 2017
Publication title -
matematika
Language(s) - English
Resource type - Journals
eISSN - 0127-9602
pISSN - 0127-8274
DOI - 10.11113/matematika.v33.n1.861
Subject(s) - group (periodic table) , combinatorics , order (exchange) , mathematics , prime (order theory) , cyclic group , natural number , characterization (materials science) , physics , abelian group , finance , quantum mechanics , economics , optics
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.