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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- Mar 13th 2013, 07:24 AMhenderson7878abstract 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.

- Mar 30th 2013, 05:23 PMjohngRe: abstract algebra: direct sums decomposition question
Here's a solution:

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