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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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    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


    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.