%0 Journal Article
%T Evaluate All the Order of Every Element in the Higher Order of Group for Addition and Multiplication Composition
%A Md. Abdul Mannan
%A Nazmun Nahar
%A Halima Akter
%A Momtaz Begum
%A Md. Amanat Ullah
%A Shabnam Mustari
%J International Journal of Modern Nonlinear Theory and Application
%P 11-30
%@ 2167-9487
%D 2022
%I Scientific Research Publishing
%R 10.4236/ijmnta.2022.112002
%X This
paper aims at treating a study on the order of every element for addition and
multiplication composition in the higher order of groups for different
algebraic structures as groups; order of a group and order of element of a
group in real numbers. Here we discuss the higher order of groups in different
types of order which will give us practical knowledge to see the applications
of the addition and multiplication composition. If <i>G</i> is a finite group, <i>n</i> is
a positive integer and</span></span><span><span><span style=\"font-family:&quot;\"> <i>a &amp;isins; G</i></span></span></span><span><span><span style=\"font-family:&quot;\">, then the order of the products <i>na</i>. When <i>G</i> is a finite group, every element must have finite order. However,
the converse is false: there are infinite groups where each element has finite
order. For example, in the group of all roots of unity in C<sup>กม</sup> each
element has finite order. Finally, we find out the order of every element of a
group in different types of higher order of group.
%K Order of Element of a Group
%K Addition Composition
%K Multiplication Composition
%K Modulo
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=118072