Finding if two groups are isomorphic

[sugarplum31]

Homework Statement

Show that the group {U(7), *} is isomorphic to {Z(6), +}

Homework Equations

The Attempt at a Solution

I drew the tables for each one. I can see that they are the same size and the identity element for U7 is 1, and for Z6 is 0. I don't really see any relationship between the two tables. I found the highest order for U7 is 7, which does not appear as an order in Z6. I thought that for two groups to be isomorphic, if one group had an element with an order of X, the other group also had to have a group with that order.

The question makes me think that the two groups ARE isomorphic since it says "show" that they are. Is it possible that they are not? Thanks for hte help!

 

[Dick]

You might want to define what U7 is. Is it the multiplicative subgroup of Z7? If so, then like Z6 it only has six elements. How can it have an element of order 7?? You should probably check your tables.