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https://doi.org/10.1007/s00009-019-1427-6

has been cited by the following article:

• TITLE: Evaluate All the Order of Every Element in the Higher Order of Group for Addition and Multiplication Composition

  AUTHORS: Md. Abdul Mannan, Nazmun Nahar, Halima Akter, Momtaz Begum, Md. Amanat Ullah, Shabnam Mustari

  KEYWORDS: Order of Element of a Group, Addition Composition, Multiplication Composition, Modulo

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.11 No.2, June 28, 2022

  ABSTRACT: 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 G is a finite group, n is a positive integer and a ⋴ G, then the order of the products na. When G 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× 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.