# Isomorphisms, Residue Classes and Multiplication Tables

Show that U(10) is isomorphic to Z_4 and write out the isomorphism explicitly.

I know that U(10) and Z_4 are both cyclic, thus they are ismorphic but for writing out the isomorphism, I need assistance.

© BrainMass Inc. brainmass.com October 9, 2019, 7:07 pm ad1c9bdddfhttps://brainmass.com/math/linear-transformation/isomorphisms-residue-classes-multiplication-tables-108494

#### Solution Preview

Z_10 = {[0], [1], ... [9]} and the subset

U(10) = {[1], [3], [7], [9]} consists of residue classes [s] mod 10 such that gcd(s, 10) = 1, where we choose representatives s between 1 and ...

#### Solution Summary

Isomorphisms, Residue Classes and Multiplication Tables are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

$2.19