What Is the Smallest Normal Subgroup of a Group Containing a Given Subset?

[norajill]

1) Let X be anon empty subset of a group G .prove that there is a smallest normal subgroup of G containing X
ii)what do we call the smallest normal subgroup of G containing X

 

[Dick]

If you want to know what something is called, I think you should look it up. If you want to know how to prove something, you should show us at least an attempt.