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Cyclic Multiplicative Group : Field of Order 2^7

1. Prove that the multiplicative group of a field of order 2^7 is cyclic.
Note: This problem can be solved in a few lines. Do not construct the field of order 2^7 to solve the problem.

2. Prove that the only subfield of a field of order is a field of order 2.


Solution Summary

A cyclic multiplicative group is investigated. The solution is detailed and well presented.