TITLE:
Evaluate All Order of Every Element of 60 and 61 Order of Group for Addition Composition
AUTHORS:
Nazmun Nahar, Md. Mehedi Hasan Modern, Abdus Salam, Md. Yousuf Miah, Shakil Ahmed, Md. Anamol Haque, Md. Abdul Mannan
KEYWORDS:
o(G), o(a), Addition Composition, Modulo, Torsion Group
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.15 No.3,
August
21,
2026
ABSTRACT: This paper aims at treating a study on the order of every element of 60 and 61 orders of group for multiplication composition. But the composition in G is associative; the multiplication composition is very significant in the order of elements of a group. We develop the order of a group, higher order of groups in different types of order and the order of elements of a group in real numbers. Let G be a group and let
a
n
∈G
be of infinite order n. In addition, notation na = e and n is a least positive integer
⇒
O(a) = n. If
a∈G
is of order n, then there exists an integer m for which
a
m
=e
if m is a multiple of n, in general we use this. Then we develop orders of elements of a cyclic group and every element of higher order of a group. After that we find out the order of every element of a group for the higher orders of the group for being binary operation.