Thread: Finitely generated

A group H is called finitely generated if there is a finite set A s.t.

Prove that every finite group is finitely generated.



I don't know how to set that up with out the { and make it smaller under the intersection.

Anyways. Can I just say the intersection of finite elements is always finite? How can this be shown?

Originally Posted by dwsmith

A group H is called finitely generated if there is a finite set A s.t.

Prove that every finite group is finitely generated.



I don't know how to set that up with out the { and make it smaller under the intersection.

Anyways. Can I just say the intersection of finite elements is always finite? How can this be shown?

I'm not really sure what you're trying to get at. The idea is that a group is generated by a subset if (roughly) all elements in the group are just products of things in the set, and things whose inverse is in the set. What if you had a finite group , what finite set has the property that every element of is a product of things in this set?

Originally Posted by dwsmith

A group H is called finitely generated if there is a finite set A s.t.

Prove that every finite group is finitely generated.



I don't know how to set that up with out the { and make it smaller under the intersection.

Anyways. Can I just say the intersection of finite elements is always finite? How can this be shown?

You can just take

Edit. Sorry Drexel28 (shouldn't that now be Maryland28?), I didn't see your reply.

Edit 2. Notice that I can make the { under the intersection smaller.