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Math Help - abstract group and field

  1. #1
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    abstract group and field

    Hi everyone
    I got this question which I dont understand:

    Identify []* as an abstract group.
    (I have already show that is a field by computing its multiplicative monoid and I get the table.)

    I am thinking of the inverse, associative and the identity which are the properties to prove that []* is a group. Is this true?
    If it is a group then what is it isomorphic to? Is it C_8? because it has 8 elements

    Thanks in advance for any idea you give
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  2. #2
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    Quote Originally Posted by knguyen2005 View Post
    Hi everyone
    I got this question which I dont understand:

    Identify []* as an abstract group.
    (I have already show that is a field by computing its multiplicative monoid and I get the table.)

    I am thinking of the inverse, associative and the identity which are the properties to prove that []* is a group. Is this true?
    If it is a group then what is it isomorphic to? Is it C_8? because it has 8 elements

    Thanks in advance for any idea you give
    A finite subgroup of the multiplicative group (of the field) is always a cyclic group.
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