Abstract
Free Group and Galois Theory are both new contents of modern mathematics with being widely studied, while there are few studies about the connections between them. We can find that the automorphisms in the definition of Galois Group is like the symbols in free group. The structure of subgroups in free groups is a significant subject which is originated from the Group Theory. Thus, this paper will introduce some basic theorems of Galois Group, free group and give a proof of the set of every subfield of a field is isomorphic to a free Galois Group.
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