|Jul18-11, 06:17 AM||#1|
Every subgroup of index 2 is normal?
I have to prove that every subgroup H of a group G with index(number of distinct cosets of the subgroup) 2 is normal.
I dont know how to start :'(
|Jul18-11, 08:28 AM||#2|
You must prove that gN=Ng for all g. But what exactly are the cosets of N??
|Jul19-11, 08:30 AM||#3|
If the element g comes from H then both gH and Hg are equal to H.
If g comes from H complement then i know it must represent the "other" coset. Since cosets partition G, i know both these cosets must be equal to H complement.
More or less correct?
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