Work

Some results on Quillen’s conjecture via equivalent-poset techniques

Year: 2024

Type: article

Abstract: We extend the main theorem of Aschbacher and Smith on the Quillen conjecture from p>5 to the remaining odd primes p = 3,5 . In the process, we develop further combinatorial and homotopical methods for studying the poset of non-trivial elementary abelian p -subgroups of a finite group. The techniques lead to a number of further results on the conjecture, often reducing dependence on the CFSG; in particular, we also provide some partial results toward the case of p=2 .

Source: Journal of Combinatorial Algebra

DOI: 10.4171/jca/95

Authors: Kevin Iván Piterman, Stephen D. Smith

Institutions: Philipps University of Marburg, University of Illinois Chicago

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Consejo Nacional de Investigaciones Científicas y Técnicas, Mathematisches Forschungsinstitut Oberwolfach, Leibniz-Gemeinschaft, Secretaría de Ciencia y Técnica, Universidad de Buenos Aires

Awards: G4651165891, G5758481953, G816603628, G846726577