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

ir Kızmaz, Muhammet Yası̇r; Yalçın, Ergün

doi:10.1090/proc/15066

Finite groups of rank two which do not involve $\mathrm {Qd}{(p)}$
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by Muhammet Yasir ir Kızmaz and Ergün Yalçın PDF

Proc. Amer. Math. Soc. 148 (2020), 3713-3721 Request permission

Abstract:

Let $p>3$ be a prime. We show that if $G$ is a finite group with $p$-rank equal to two, then $G$ involves $\text {Qd}{(p)}$ if and only if $G$ $p’$-involves $\text {Qd}{(p)}$. 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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