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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"

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# Normal groups

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