Thread: 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

Originally Posted by knguyen2005

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.