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Prove H G iff when a,b are element of H ab 1 is an element of H note the negative one is exponent ob b means the inverse of Decide if each of the following is true of if it is

2)Prove H<= G iff when a,b are element of H, ab^-1 is an element of H . (note: the negative one is exponent ob b means the inverse of b). 3) Decide if each of the following is true of if it is false. If true, give a proof, if false, give a counterexample. a)Let H<= G and suppose a and b are elements of G. Then a^2 H = b^2 H. b)If ac _= bc (mod N) and c different 0, then a = b(mod n). c) Any subgroup of index 2 is normal.

Apr 30 2020 View more View Less

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