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Ant farm
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Hi There,
Ok, I'm new to this so I'm sorry if this is abit warbled!...
We have a normal subgroup N of a finite group H such that [H:N]=2
We have a chatacter Chi belonging to the irreducible characters of H, Irr(H) , which is zero on H\N.
I have already shown that Chi restricted to N = Theta 1 + Theta 2, Where
Theta 1 is not equal to Theta 2, and both Theta 1, and Theta 2 belong to Irr(N).
I am now trying to show that given a conjugacy class K of H which is also a conjugacy class of N, we get Theta 1 (n) = Theta 2 (n) for n a member of K.
Intuitively, I can see this is true, I have seen examples in the alternating group A6, the normal subgroup of index 2 in S6 fro example.
I would be really greatful for a push in the right direction...I have books: 'James and Liebeck' and 'Isaacs'... if you could even direct me to some relevant info?
Wow, think my notation is abit crap, sorry.
Ok, I'm new to this so I'm sorry if this is abit warbled!...
We have a normal subgroup N of a finite group H such that [H:N]=2
We have a chatacter Chi belonging to the irreducible characters of H, Irr(H) , which is zero on H\N.
I have already shown that Chi restricted to N = Theta 1 + Theta 2, Where
Theta 1 is not equal to Theta 2, and both Theta 1, and Theta 2 belong to Irr(N).
I am now trying to show that given a conjugacy class K of H which is also a conjugacy class of N, we get Theta 1 (n) = Theta 2 (n) for n a member of K.
Intuitively, I can see this is true, I have seen examples in the alternating group A6, the normal subgroup of index 2 in S6 fro example.
I would be really greatful for a push in the right direction...I have books: 'James and Liebeck' and 'Isaacs'... if you could even direct me to some relevant info?
Wow, think my notation is abit crap, sorry.