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I try to prove it, but I can't. Please tell it true or false?

Let a group $G=G_1\times G_2$, i.e. $G$ is direct product of $G_1$ and $G_2$.

If $H$ is normal subgroup of $G$, then $H$ will be direct product of $H_1$ and $H_2$, for $H_1$, $H_2$ are normal subgroup $G_1$ and $G_2$, isn't it?

  • 1
    No. Read the answer below.2012-09-05

3 Answers 3