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I'm sorry if this question doesn't fit with MO rules, but I've asked on Math SE yet without answers, so I post here with the hope someone will answer me.

I want to show, knowing the Goursat's theorem, that given two groups $G, G'$ and a subgroup $H \subset G\times G'$, the projections $p_1: H \rightarrow G $ and $p_2:H \rightarrow G' $ are surjective (this is the subdirect product) iff $(H,p_1,p_2)$ is a fiber product.

Also: there is a kind of paper or reference or knowledge somewhere which tells about the Griess notation of subdirect product?

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  • $\begingroup$ You should explain what you have tried so far (it indeed belongs to StackExchange rather than here). Also please provide the MathSE link. $\endgroup$
    – YCor
    Nov 2, 2015 at 11:00
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    $\begingroup$ As it says on the linked Wikipedia page, this is an immediate consequence of Goursat's Theorem! $\endgroup$
    – Derek Holt
    Nov 2, 2015 at 11:09

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