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Cohomology of Burnside Rings

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

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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

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