- #1
ttm7nana
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Hello, I am having trouble with the following problem.
Suppose that H is a subgroup of G such that whenever Ha≠Hb then aH≠bH. Prove that gHg^(-1) is a subset of H.
I have tried to manipulate the following equation for some ideas
H = Hgg^(-1) = gg^(-1)H
but I don't know how to go from here. I can't figure out how I can use the conditions to show that every element in gHg^(-1) is also in H.
I also know that gHg^(-1) is a subgroup of G, but I don't know if this fact can be used here.
It well be great if someone can point me in the right direction. Thank you.
Suppose that H is a subgroup of G such that whenever Ha≠Hb then aH≠bH. Prove that gHg^(-1) is a subset of H.
I have tried to manipulate the following equation for some ideas
H = Hgg^(-1) = gg^(-1)H
but I don't know how to go from here. I can't figure out how I can use the conditions to show that every element in gHg^(-1) is also in H.
I also know that gHg^(-1) is a subgroup of G, but I don't know if this fact can be used here.
It well be great if someone can point me in the right direction. Thank you.