normal subgroup

apple2009 · #1 $Old$ November 4th, 2009, 05:58 PM

If H is a subgroup of a finite group G of index [G: H] two, then H is normal in G.

aman_cc · #2 $Old$ November 4th, 2009, 07:09 PM

Quote:

Originally Posted by apple2009 $View Post$

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.

apple2009 · #3 $Old$ November 5th, 2009, 07:57 PM

Quote:

Originally Posted by aman_cc $View Post$

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?

apple2009 · #4 $Old$ November 8th, 2009, 05:30 PM

what is the two left and right coset there?