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    Group Theory

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    Let G be a group, let a, b be elements in G and let m and n be (not necessarily positive) integers.

    Prove that:

    i) (a^n)^m= (a^mn)
    ii) if a and b commute, then (ab)^n = a^n times b^n
    iii) a^m times a^n = (a)^(m+n)

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    Solution Summary

    Group theory proofs are provided using a case-by-case approach.