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.
Evaluate all order of every element of higher 100, 105 and 107 order of group for multiplication composition
Authors
- Md. Abdul Mannan Department of Mathematics, Uttara University, Dhaka, Bangladesh.
- Kanchon Kumar Bishnu Department of Computer Science, California State University, Los Angeles, California, USA.
- Shoma Islam Department of Management Information Systems, International American University, Los Angeles, USA.
- Md. Shafiul Alam Chowdhury Department of Computer Science and Engineering, Uttara University, Dhaka, Bangladesh.
- Md. Amzad Hossain Department of Education, Uttara University, Dhaka, Bangladesh.
- Md. Shafikul Islam Department of Computer Science and Engineering, Uttara University, Dhaka, Bangladesh.
- Sahib Jada Eyakub Khan Biman Bangladesh Airlines, Kurmitola, Dhaka, Bangladesh.
- Hashiara Khatun Department of Health Science, Panola College, Carthage, Texas, USA.
