# Definition talk:Internal Group Direct Product

But this is clear from the definition of the subgroup—you're doubling it here! Please kindly reconsider your view on this matter—those restrictions don't bring anything new: if you'd like to leave them as they are then you could resign from the word "subgroup" there and say something like "Let $H$ be a subset of a group $\left({G, \circ}\right)$. Taking restriction $\circ \restriction_H$ of $\circ$ to $H$ makes $H$ a group with this operation, i.e. $\left({H, \circ \restriction_H}\right)$ is a group." This group is a subgroup of $\left({G, \circ}\right)$. But this is pointed out in the article about subgroup definition, not explicitly and maybe herein lies the problem. joel talk 19:06, 29 December 2012 (UTC)