Finite groups of rank two which do not involve $Qd(p)
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-$p$ homo...
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| creator | Kızmaz, Muhammet Yasir Yalcin, Ergun |
| description | 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 $p
\leq 3$. |
| doi_str_mv | 10.48550/arxiv.1812.10810 |
| format | Article |
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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
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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
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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
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| subjects | Mathematics - Algebraic Topology Mathematics - Group Theory |
| title | Finite groups of rank two which do not involve $Qd(p) |
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