A Represent of Generators of the Cyclic Group of Higher Even, Odd and Prime Order for Composition Being Multiplication  

作　　者：Faruque Hossain Mozumder Md. Sahidul Islam Md. Mehedi Hasan Modern Md. Abdul Mannan Faruque Hossain Mozumder;Md. Sahidul Islam;Md. Mehedi Hasan Modern;Md. Abdul Mannan(ICT Division Jamuna Bank PLC, Dhaka, Bangladesh;Department of Physics, Govt. H. S. S College, Magura, Bangladesh;Department of Mathematics, Uttara University, Dhaka, Bangadesh)

机构地区：[1]ICT Division Jamuna Bank PLC, Dhaka, Bangladesh [2]Department of Physics, Govt. H. S. S College, Magura, Bangladesh [3]Department of Mathematics, Uttara University, Dhaka, Bangadesh

出　　处：《Journal of Applied Mathematics and Physics》2024年第12期4198-4205,共8页应用数学与应用物理(英文)

摘　　要：This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and generators of the cyclic group in real numbers. Also we express cyclic and generators of the group for composition in real numbers. Here we discuss the higher order of groups in different types of order, and generators of the cyclic group which will give us practical knowledge to see the applications of the composition. In order to find out the order of an element am∈Gin which an=e= identity element, then find Highest Common Factor i.e. (H.C.F) of mand n. When Gis a finite group, every element must have finite order but the converse is false. There are infinite groups where each element has a finite order. There may be more than one generator of a cyclic group. Also every cyclic group is necessarily abelian. But show that every infinite cyclic group contains only two generators. Finally, we find out the generators of the cyclic group of higher even, odd and prime order in different types of the group for composition being multiplication.This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and generators of the cyclic group in real numbers. Also we express cyclic and generators of the group for composition in real numbers. Here we discuss the higher order of groups in different types of order, and generators of the cyclic group which will give us practical knowledge to see the applications of the composition. In order to find out the order of an element am∈Gin which an=e= identity element, then find Highest Common Factor i.e. (H.C.F) of mand n. When Gis a finite group, every element must have finite order but the converse is false. There are infinite groups where each element has a finite order. There may be more than one generator of a cyclic group. Also every cyclic group is necessarily abelian. But show that every infinite cyclic group contains only two generators. Finally, we find out the generators of the cyclic group of higher even, odd and prime order in different types of the group for composition being multiplication.

关 键 词：Order of Element of a Group Multiplication Composition Highest Common Factor Generator 

分 类 号：O15[理学—数学]