White Rose University Consortium logo
University of Leeds logo University of Sheffield logo York University logo

Cohomology of Burnside Rings

Harrington, Benen (2018) Cohomology of Burnside Rings. PhD thesis, University of York.

This is the latest version of this item.

[img]
Preview
Text
the.pdf - Examined Thesis (PDF)
Available under License Creative Commons Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales.

Download (500Kb) | Preview

Abstract

We study the Ext groups groups Ext^l_A(G) (Z_H , Z_J ) where A(G) is the Burnside ring of a finite group G and for a subgroup H ⊂ G, the A(G)-module Z_H is defined by the mark homomorphism corresponding to H. If |G| is square-free we give a complete description of these groups. If |G| is not square-free we show that for certain H, J ⊂ G the groups Ext^l_A(G)(Z_H , Z_J ) have unbounded rank. We also extend some of these results to the rational and complex rep- resentation rings of a finite group, and describe a new generalisation of the Burnside ring for infinite groups.

Item Type: Thesis (PhD)
Academic Units: The University of York > Mathematics (York)
Identification Number/EthosID: uk.bl.ethos.767308
Depositing User: Mr Benen Harrington
Date Deposited: 01 Mar 2019 14:44
Last Modified: 19 Feb 2020 13:07
URI: http://etheses.whiterose.ac.uk/id/eprint/22837

Available Versions of this Item

  • Cohomology of Burnside Rings. (deposited 01 Mar 2019 14:44) [Currently Displayed]

You do not need to contact us to get a copy of this thesis. Please use the 'Download' link(s) above to get a copy.
You can contact us about this thesis. If you need to make a general enquiry, please see the Contact us page.

Actions (repository staff only: login required)