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## Homework Statement

Prove or disprove U(20) and U(24) are isomorphic

## Homework Equations

## The Attempt at a Solution

U(20)={1,3,,7,9,11,13,17,19}

U(24)={1,5,7,11,13,17,19}

In U(20), Order(1)=1 Order(3)=4 Order(7)=4 Order(9)=2, Order(11)=2 Order(13)=4, Order(17)=4, Order(19)=2

In U(24), Order(1)= 1 , Order(5)=2 , ORder(7)=2, Order(11)=2 , Order(13)=2 , Order(17)=2, Order(19)= 2

Since each of the elements in each of the groups do not generate the same order for each elements in the opposite group, can't I conclude thatt U(24) and U(20) are not isomorphic?