# To prove that G is a cyclic group of order n

Modern Algebra

Group Theory (I)

G contains all symbols a^i, i = 0,1,2,......., n - 1 where we insist that

a^0 = a^n = e, a^i.a^j = a^(i + j) if i + j < or equal to n and a^i.a^j = a^(i + j - n) if i + j > n .

Prove that G is a cyclic group of order n.

The fully formatted problem is in the attached file.

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The solution of the Posting is in the attached file.

Modern Algebra

Group Theory (I)

By:- Thokchom Sarojkumar Sinha

contains all symbols where we insist that

if and if .

Prove that is a cyclic group of order .

Solution:- Here

where

The operation '.' in is defined as

The composition table is given below:

...

#### Solution Summary

A composition table is used to provide a proof regarding the cyclic nature of a group. The solution is detailed and well presented.