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Groupprops β

Minimal splitting field



Let G be a finite group and K be a field whose characteristic does not divide the order of G (so K may have characteristic zero or some prime coprime to the order of G). We say that K is a minimal splitting field for G if K is a splitting field for G and no proper subfield of K is a splitting field for G.


Uniqueness and relation with field generated by character values

Relation with sufficiently large fields and cyclotomic fields