The mod 2 cohomology rings of the alternating subgroups of the Coxeter groups of Type B

2023/12/19 by Lorenzo Guerra, Guerra, Lorenzo, Santanil Jana +1
Mathematics · #20J06 (Primary) 13A50 #55N10 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2312.12346

openalex publication_date 2023/12/19 · openalex created_date 2023/12/22 · openalex updated_date 2026/07/28

Abstract

We show that the direct sum of the cohomology groups of the alternating subgroups of the family of Coxeter groups of Type B exhibits an almost-Hopf ring structure. We apply techniques developed by Giusti and Sinha to fully compute a presentation of this structure for mod 2 coefficient.

Related

• Mod-two cohomology rings of alternating groups
• The cohomology of the Lyons group and double covers of alternating groups
• The cohomology of the McLaughlin group and some associated groups
• The mod 2 cohomology rings of congruence subgroups in the Bianchi groups
• Invariants cohomologiques mod 2 et invariants de Witt des groupes alternés