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Abstract
The objective of the paper is to present applications of Lagrange’s theorem, order of the element, finite group of order, converse of Lagrange’s theorem, Fermats little theorem and results, we prove the first fundamental theorem for groups that have finite number of elements. In this paper we show with the example to motivate our definition and the ideas that they lead to best results. It can be used to prove Fermat's little theorem and its generalization, Euler's theorem. These special cases were known long before the general theorem was proved. In this paper some Corollaries gives the famous result called the Fermat’s Little Theorem. In this paper we see that given a subgroup H of a group G, it may be possible to partition the group G into subsets that are in some sense similar to H itself
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