Thread: 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

is a subset of if every element of is an element of .

is a subgroup of if is a subset of and is a group.

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