# Math Help - subset

1. ## subset

may i know what is the different between the subgroup <H> of G and the subset H of G.

i dont really get what it means for
the subgroup <H> conincides with the intersection of all subgroups of G which contain the subset H

2. $H$ is a subset of $G$ if every element of $H$ is an element of $G$.

$H$ is a subgroup of $G$ if $H$ is a subset of $G$ and $H$ is a group.

The subgroup generated by $H$ is the smallest subgroup of $G$ containing $H$. Informally, you need to throw as little "stuff" as possible into $H$ until you get a group. More formally, take the intersection of all subgroups of $G$ containing $H$. Since arbitrary intersections of a group form a group, you get the smallest subgroup of $G$ that contains $H$.