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Math Help - Algebra question

  1. #1
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    Algebra question

    Hi guys,

    I am working on an algebra problem and am not quite sure if this is right. It "feels" correct but at the same time I kind of feeling like I might be begging the question.


    \text{\underline{Theorem:} Let G be a group with the following property:} \text{Whenever <br />
a, b, c} \in \text{G and a*b = c*a implies b = c, then G is Abelian}

    \text{\underline{Proof:} Suppose a*b = c for some a, b, c } \in \text{ G.Applying a both sides by a on the right gives a*b*a = c*a.}
    \text{The associative property of groups gives a*(b*a) = c*a. <br />
By hypothesis,}
    \text{we can cancel a from both sides <br />
yielding b*a = c. <br />
Hence, b*a = c} \text{and a*b = c <br />
implies a*b = b*a. Therefore, G is Abelian.} \blacksquare
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  2. #2
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    Looks good to me.
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