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Math Help - is it abelian

  1. #1
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    is it abelian

    hey, G is a group such that o(G) = 36. Then is G abelian.
    I knw that if o(G) = p^2 where p is a prime, then G is abelian. But here
    o(G)=2^2 * 3^2. So what can I say about G.
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  2. #2
    Senior Member Dinkydoe's Avatar
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    This is no pre-university math.

    Observe that G has sylow-p subgroups |H_1|= 3^2, |H_2| = 2^2, which are as you stated abelian.

    Since both groups are abelian we have H_1 \triangleleft G and H_2  \triangleleft G. Now it follows that G \cong H_1\times H_2. ( trivially it follows that G is abelian)
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