Normal subgroups?

  • Thread starter raj123
  • Start date
  • #1
16
0

Main Question or Discussion Point

Normal subgroups??

Normal subgroups?
 
Last edited:

Answers and Replies

  • #2
matt grime
Science Advisor
Homework Helper
9,395
3
H is normal if gHg^(-1)=H for all g. If H is a subgroup of some order, then so is gHg^(-1). End of hint.
 
  • #3
brownnrl
Ah so

If H is unique subgroup of order n (no others) it must be normal as all other xHx^(-1) must be of that same order n.

I was thrown by the 10 or 20 in the problem, but it could really be any order n.

Thank you very much for the hint. I saw the disclaimer after I posted about the homework, so I'm sorry if this question wasn't up to par.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,833
956
Also, a subgroup, H, of a group, G, is a normal subgroup if and only if the "left cosets" and "right cosets" are the same. A result of that is that we can define the group operation on the cosets (if p is in coset A and q is in coset B then AB is the coset that contains pq) in such away that the collection of cosets is a group in its own right: G/H.
 

Related Threads on Normal subgroups?

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
12
Views
3K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
3K
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
11
Views
4K
  • Last Post
Replies
5
Views
5K
Top