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

Muhammet Yasir Kızmaz; Ergun Yalcin

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

Group Theory 2020-06-25 v2 Algebraic Topology

Authors: Muhammet Yasir Kızmaz , Ergun Yalcin

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 $p \leq 3$ .

Keywords

finite groups finite group theory group theory

Cite

@article{arxiv.1812.10810,
  title  = {Finite groups of rank two which do not involve $Qd(p)$},
  author = {Muhammet Yasir Kızmaz and Ergun Yalcin},
  journal= {arXiv preprint arXiv:1812.10810},
  year   = {2020}
}

Comments

Revised version, to appear in Proc. Amer. Math. Soc

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

Abstract

Keywords

Cite

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