Group of Units U(n) Isomorphism Classes as External Direct Products
In Group Theory from Abstract Algebra, U(n) is the group of units under multiplication mod n. It contains the positive integers less than n that are relatively prime to n. If n is written as a product of relatively prime factors, then U(n) is isomorphic to the external direct product of the U-groups for those factors. For factors that are prime powers, we can relate these to cyclic groups ℤm.
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(0:00) U(n) external direct product isomorphism theorem (related to relatively prime factors of n)
(1:15) U(p^n) isomorphism classes when p is prime
(3:22) U(8), U(16), U(32), U(64) isomorphism classes (non-cyclic groups)
(4:40) U(3), U(9), U(27) isomorphism classes (cyclic groups)
(6:21) U(125) isomorphism class
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