- #1
Marin
- 193
- 0
Hi!
I want to determine which of the subgropus of the symmetric group S(3) are normal. The condition is:
for every g in G: g H g^-1 = H where H is a subgroup of G.
I have determined all the subgroups of S(3) and I came up with 13.
What I did after that is I considered 2 cases:
1: g is elem. of H, then g^-1 is also in H and the condition is satisfied.
2: g is not el. of H, but still el. of G, the same is true for g^-1.
then I got stuck :(
theoretically all the subgroups could be examined one by one, but it seems to me somehow too long and "not mathematical"
Does anyone know a better way?
thanks in advance!
° and another question: If H is a normal subgroup of G, what should one understand under "G modulo H"
I want to determine which of the subgropus of the symmetric group S(3) are normal. The condition is:
for every g in G: g H g^-1 = H where H is a subgroup of G.
I have determined all the subgroups of S(3) and I came up with 13.
What I did after that is I considered 2 cases:
1: g is elem. of H, then g^-1 is also in H and the condition is satisfied.
2: g is not el. of H, but still el. of G, the same is true for g^-1.
then I got stuck :(
theoretically all the subgroups could be examined one by one, but it seems to me somehow too long and "not mathematical"
Does anyone know a better way?
thanks in advance!
° and another question: If H is a normal subgroup of G, what should one understand under "G modulo H"