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Group of Units of a set

  1. Jun 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Theorm 1: If M is a monoid, the set of M* of all units in M is a group using the operation of M, called the group of units of M.

    My question is this always a "real" group? for example, is this 'group' always closed under the binary operation?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jun 23, 2014 #2
    Yes. Try to prove it!
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