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

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


    is a subgroup of


    For is prime.



    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.