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    The Group Theory Concept: The Abelian Group

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    Please address the following problem: A group of order p^2,where p is a prime number, is abelian.

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    https://brainmass.com/math/group-theory/group-theory-concept-abelian-group-65235

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    A group of order ,where is a prime number, is abelian.

    Solution:- Let be a group of order , that is .

    Then

    is a subgroup of

    and

    Hence
    For is prime.

    Suppose

    Then

    which imply that there exists such that .

    is a proper subgroup of

    For by assumption.

    But is a subgroup of

    ...

    Solution Summary

    In this solution, a detailed, step-wise response has been constructed to illustrate how to conduct a proof to show that something is abelian. The solution is detailed and well presented in an attached Word document.

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