The multiplicative group $ \mathbb {{F}^{\times}_{7}}$ is isomorphic to a subgroup of the multiplicative group $ \mathbb {{F}^{\times}_{31}}$.
Can anyone tell me this statement is true or false. Please explain your answer. I am new to algebra.
[Math] The multiplicative group $ \mathbb {{F}^{\times}_{7}}$ is isomorphic to a subgroup of multiplicative group $ \mathbb {{F}^{\times}_{31}}$
abstract-algebragroup-isomorphismgroup-theory
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Best Answer
Yes, it is true. The group $\mathbb{Z}_7^\times$ is a cyclic group of order $6$ (it is generated by $3$). And the group $\mathbb{Z}_{31}^\times$ has an element of order $6$, which is $6$.