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Two remarks on the group algebra of a finite group

Two remarks on the group algebra of a finite group

If <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K subset-of-or-equal-to upper Q left-parenthesis zeta Subscript m Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>K</mml:mi> <mml:mo>⊆<!-- ⊆ --></mml:mo> <mml:mi>Q</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>ζ<!-- ζ --></mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">K \subseteq Q({\zeta _m})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <italic>m</italic> least, we find the …