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

2018/12/27 by M. Yasi̇r Kızmaz, Kızmaz, Muhammet Yasir, Ergün Yalçın +1
Mathematics · #57S17 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Primary: 20Dxx #Secondary: 20E25

paper · pdf · doi:10.48550/arxiv.1812.10810

openalex publication_date 2018/12/27 · openalex created_date 2019/01/11 · openalex updated_date 2026/07/28

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 ≤ 3.

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