Abstract Algebra: define an operation

  • Thread starter murmillo
  • Start date
  • #1
118
0

Homework Statement


Does the rule g*x = xg^-1 define an operation of G on G?


Homework Equations





The Attempt at a Solution


I don't even know what this means. Could someone just tell me what it means for a rule to define an operation of one group on itself? I should be able to figure it out from there.
 

Answers and Replies

  • #3
118
0
Oh, I see. OK, thanks, I can take it from here.
 
  • #4
Delta2
Homework Helper
Insights Author
Gold Member
3,609
1,397
So you have to prove that (gh)*x=g*(h*x)
[tex](gh)*x=x(gh)^{-1}=x(h^{-1}g^{-1})=(xh^{-1})g^{-1}=(h*x)g^{-1}=g*(h*x)[/tex]
 

Related Threads on Abstract Algebra: define an operation

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
5
Views
778
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
1
Views
865
Top