Papers
arxiv:2308.12286
Fixed point conditions for non-coprime actions
Published on Aug 23, 2023
Authors:
Abstract
In the setting of finite groups, suppose J acts on N via automorphisms so that the induced semidirect product Nrtimes J acts on some non-empty set Omega, with N acting transitively. Glauberman proved that if the orders of J and N are coprime, then J fixes a point in Omega. We consider the non-coprime case and show that if N is abelian and a Sylow p-subgroup of J fixes a point in Omega for each prime p, then J fixes a point in Omega. We also show that if N is nilpotent, Nrtimes J is supersoluble, and a Sylow p-subgroup of J fixes a point in Omega for each prime p, then J fixes a point in Omega.
Models citing this paper 0
No model linking this paper
Cite arxiv.org/abs/2308.12286 in a model README.md to link it from this page.
Datasets citing this paper 0
No dataset linking this paper
Cite arxiv.org/abs/2308.12286 in a dataset README.md to link it from this page.
Spaces citing this paper 0
No Space linking this paper
Cite arxiv.org/abs/2308.12286 in a Space README.md to link it from this page.
Collections including this paper 0
No Collection including this paper
Add this paper to a
collection
to link it from this page.