Central product

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In group theory a group G is the central product of two of its subgroups G₁ and G₂ if the following hold:

• G = G₁ G₂
• For all and
• is contained in the center of G.

A sufficient condition for G to be the central product of G₁ and G₂ is that G is isomorphic to the direct product of G₁ and G₂.