If H is a subgroup of a finite group G of index [G: H] two, then H is normal in G.
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Originally Posted by apple2009 If H is a subgroup of a finite group G of index [G: H] two, then H is normal in G. Hint - What can you say about right and left cosets of H? And, hence about H.
Originally Posted by aman_cc Hint - What can you say about right and left cosets of H? And, hence about H. To prove for normal, I need to have the right cosets equal to right cosets, is the two left cosets are the cyclic and I?
what is the two left and right coset there?
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