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edited Apr 13, 2017 at 12:58

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Yes (Hirshon), even if $G_1, G_2$ are not finite.

Related: Can we ascertain that there exist an epimorphism $G\rightarrow H?$Can we ascertain that there exist an epimorphism $G\rightarrow H?$

Cancellation theorem for direct and other kinds of products between groups Cancellation theorem for direct and other kinds of products between groups

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created Dec 7, 2013 at 13:21

Torsten Schoeneberg

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Yes (Hirshon), even if $G_1, G_2$ are not finite.

Related: Can we ascertain that there exist an epimorphism $G\rightarrow H?$

Cancellation theorem for direct and other kinds of products between groups