<p>We prove a specific case of Rubin’s saturation conjecture about the realization of <i>G</i>-transfer systems, for <i>G</i> a finite cyclic group, by linear isometries <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_377_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(N_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation>-operads, namely the case of cyclic groups of order <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_377_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(p^nq^m\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>p</mi> <mi>n</mi> </msup> <msup> <mi>q</mi> <mi>m</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> for <i>p</i>,&#xa0;<i>q</i> distinct primes and <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40062_2025_377_Article_IEq7.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="67" /> </InlineMediaObject> <EquationSource Format="TEX">\(n,m\in \mathbb {N}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Realization of saturated transfer systems on cyclic groups of order \(p^nq^m\) by linear isometries \(N_\infty \)-operads

  • Julie Bannwart

摘要

We prove a specific case of Rubin’s saturation conjecture about the realization of G-transfer systems, for G a finite cyclic group, by linear isometries \(N_\infty \) N -operads, namely the case of cyclic groups of order \(p^nq^m\) p n q m for pq distinct primes and \(n,m\in \mathbb {N}\) n , m N .