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Math Help - abstract algebra: direct sums decomposition question

  1. #1
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    abstract algebra: direct sums decomposition question

    If H, K◅ G are simple groups, G=HK, and H ∩ K=<e>, show that either H ≅K≅ Z_p for p a prime, or N◅ G ⇒N=<e>, H, K, or G.
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  2. #2
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    Re: abstract algebra: direct sums decomposition question

    Here's a solution:

    abstract algebra: direct sums decomposition question-mhfgroups2.png
    Thanks from henderson7878
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