Explore BrainMass
Share

Isomorphisms, Residue Classes and Multiplication Tables

This content was STOLEN from BrainMass.com - View the original, and get the solution, here!

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 September 23, 2018, 7:48 pm ad1c9bdddf - https://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