Evaluate all order of every element of higher 100, 105 and 107 order of group for multiplication composition

Md. Abdul Mannan (), Kanchon Kumar Bishnu (), Shoma Islam (), Md. Shafiul Alam Chowdhury (), Md. Amzad Hossain (), Md. Shafikul Islam (), Sahib Jada Eyakub Khan () and Hashiara Khatun ()

Edelweiss Applied Science and Technology, 2025, vol. 9, issue 7, 835-850

Abstract: This paper aims at treating a study on the order of every element of higher 100, 105, and 107 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 o(G), higher order of groups in different types of order and the order of elements o(a) of a group in real numbers. Let G be a group and let a^n ∈ G be of infinite order n, then find Highest Common Factor (i.e., (n, m) denotes H.C.F of n and m). The Highest Common Factor of two numbers is the “smallest non-zero common number” which is a multiple of both the numbers. So o(a^m) = n / H.C.F(n, m), where (n, m) denotes the H.C.F of n and m. 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.

Keywords: Multiplication Composition; Torsion Group; H.C.F.; o(G); o(a) (search for similar items in EconPapers)
Date: 2025
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