• Support PF! Buy your school textbooks, materials and every day products Here!

Anstract Algebra proof - cosets

  • Thread starter kathrynag
  • Start date
  • #1
598
0

Homework Statement


Let H be a subgroup of G such that g^-1hg is an element of H for all g in G and all h in H. Show that every left coset gH is the same as the right coset Hg.


Homework Equations





The Attempt at a Solution


need to show gh1=h2g
I know I need to show this, but am unsure on how to.
 

Answers and Replies

  • #2
598
0
I know the whole set up excpet for this part and it confuses me.
 
  • #3
139
12
Let g be in G, h in H (sorry, Latex seems to be failing presently). As you say, you need to show that there exists k in H such that
gh = kg. You know that ghg-1 = k is in H. Rearrange this to get something useful.
 
  • #4
598
0
Oh, that makes sense
 

Related Threads for: Anstract Algebra proof - cosets

  • Last Post
Replies
2
Views
980
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
1
Views
833
  • Last Post
Replies
2
Views
4K
Replies
3
Views
2K
Replies
3
Views
915
Replies
2
Views
320
Replies
1
Views
3K
Top