Question

Show that the multiplicative group Z₁₁^x is isomorphic to the additive group Z₁₀. Please show me how to find the multiplicative group Z₁₁^x

Answer 1

zt = { all those elements ofz, in which mulhplicative - inverse enest 211 = {oli2..- lo] in zil o does not inverse with respect S to mulhplicative 211 = {12).- 103 210= {0,12. g} with respect to C addition For isomorphuc zit in Isore orphic to zio in their enist an Iso- - morphisme between zo to zit ut g: Zio - 24 x 0 1 2 3 4 5 6 78 9 g(+) 12 4 8 5 10 9736 Debine 9(4) = 24 modell 9 (x+y) = g(x) + g(y) for homomophon $(x+y) = 2*+y wodini = 2.24 mod 11 1. = g(1) g(y) = g us an homomorphism

1) к= { : 3%- 42 хар g®) о - 2* me i = 1 X= kaj = {+} - за 1- & both on finute of some no. of element so, outo g is an isomorphusm Z10 71