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arXiv · 1812.10810

Finite groups of rank two which do not involve $Qd(p)$

Muhammet Yasir Kızmaz·Ergun Yalcin
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Abstract

Let $p>3$ be a prime. We show that if $G$ is a finite group with $p$-rank equal to 2, then $G$ involves $Qd(p)$ if and only if $G$ $p'$-involves $Qd(p)$. This allows us to use a version of Glauberman's ZJ-theorem to give a more direct construction of finite group actions on mod-$p$ homotopy spheres. We give an example to illustrate that the above conclusion does not hold for $p \leq 3$.

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Muhammet Yasir Kızmaz, Ergun Yalcin. 2018-12-27. Finite groups of rank two which do not involve $Qd(p)$. https://arxiv.org/abs/1812.10810

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