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$p$th powers of distinguished subfields

$p$th powers of distinguished subfields

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k superset-of s superset-of k 0"> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>⊃</mml:mo> <mml:mi>s</mml:mi> <mml:mo>⊃</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>k</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">k \supset s \supset {k_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be fields of characteristic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p not-equals 0 comma k slash k 0"> …