Using permutation group notation:
Question 1: Is e, (12)(34), (13)(24), (14)(23) a representation of C2 x C2? [Note C2 = cyclic group of order 2.]
Question 2: Is C2 x C2 the group of symmetries of the following 4 numbers (viewed as roots of a polynomial with coefficients in Z)?
Question 3: If the above 2 assertions are correct, then can I conclude that C2 x C2 is the Galois Group of the polynomial:
(x^2 - 2x - 1)(x^2 - 2x - 2) = (x^4 - 4x^3 +x^2 + 6x + 2)?
(since the first quadratic has (as roots) the first 2 numbers listed, and the 2nd
quadratic has the latter 2)