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To prove that G is a cyclic group of order n

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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.

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

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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 provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
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