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- Thread starter Newtime
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quasar987

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This holds for any group. Were you looking for a sharper result specifically in the case where N=[G,G]=G' (the derived subgroup)?

As for your second question, it is not difficult and you should try answering it yourself by splitting the problem into simpler ones:

A) Show (GxH)/(NxM) ~ (G/N) x (H/M) for any group G,H and normal subgroups N,M (where ~ means isomorphic)

B) Show (GxH)'=G'xH' for any groups G,H

C) Conclude from this.

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This holds for any group. Were you looking for a sharper result specifically in the case where N=[G,G]=G' (the derived subgroup)?

As for your second question, it is not difficult and you should try answering it yourself by splitting the problem into simpler ones:

A) Show (GxH)/(NxM) ~ (G/N) x (H/M) for any group G,H and normal subgroups N,M (where ~ means isomorphic)

B) Show (GxH)'=G'xH' for any groups G,H

C) Conclude from this.

Thanks for the help; you've given me some good stuff to work out, and it looks like the result I was looking for is not only true, but shouldn't be too hard to prove.

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