Assume that [itex]G[/itex] is some group with two normal subgroups [itex]H_1[/itex] and [itex]H_2[/itex]. Assuming that the group is additive, we also assume that [itex]H_1\cap H_2=\{0\}[/itex], [itex]H_1=G/H_2[/itex] and [itex]H_2=G/H_1[/itex] hold. The question is that is [itex]G=H_1\times H_2[/itex] the only possibility (up to an isomorphism) now?(adsbygoogle = window.adsbygoogle || []).push({});

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# Two quotient groups implying Cartesian product?

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