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

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- Feb 4th 2011, 08:11 AMalexandrabel90subset
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 - Feb 4th 2011, 01:14 PMDrSteve
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 .