Find an isomorphism from the Klein 4-group to the group .2f1;2g ; /.

Week 1 BASICS REWIEW Arithmetic: a+b=b+a a+b +c=a+(b+c) ab+c =ab+ac ab=ba ab)c=a(bc) Multiplying Fractions: a c ac × = b d bd Dividing Fractions: a÷ = ad b d bc Adding Fractions: a+ = ad+cb= ad+bc b d bd bd bd Exponent Basics: an means multiply a by itself n times 0 =0wheren>0 0 a =1wherea≠0 0 isindeterminate a = 1 wherea≠0 an becau0e n−n n −n 1=a =a =a a 1=a a−n 1 =a−n an Laws of Exponents: Given m & n are integers and a & b are real numbers: a a =a m+n m a m−n n =a wherea≠0 a a a m (¿¿n) n mn (¿¿ m) =a =¿ ¿ n n n (ab) =a b a n an ( ) = nwhereb≠0 b b −n n n ( ) =( ) = b b a an Root Basics: 1 n n √a=a na =( a) m √ √ 3 o Ex. Calculate 2 . 8 3 2 3 2 We would rather do (√8) than do √8 . Root Laws: 1 1 1 √ab=(ab) =a b = a √ √n 1 1 n n na =( ) = a = √a √b b 1 √b bn Factoring Formulas: