Permutation Group Proof

  • #1

Homework Statement


Suppose G is a group, H < G (H is a subgroup of G), and a is in G.

Prove that a is in H iff <a> is a subset of H.


Homework Equations


<a> is the set generated by a (a,aa,aa^-1,etc)


The Attempt at a Solution


For some reason this seems too easy:

1. Suppose a is in H.
Since H is a group, a^-1 is in H.
Since H is a group aa, is in H (as is aa^-1, etc.)
Thus <a> is a subset of H.

2. Suppose <a> is a subset of H.
Obviously a is in H.

And this completes the proof... or am I missing something?
 

Answers and Replies

  • #2
shameful bump
 

Related Threads on Permutation Group Proof

  • Last Post
Replies
5
Views
4K
Replies
4
Views
622
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
2
Replies
25
Views
3K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
7
Views
786
Top