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Title: Cohomology of Burnside rings
Author: Harrington, Benen
ISNI:       0000 0004 7658 8082
Awarding Body: University of York
Current Institution: University of York
Date of Award: 2018
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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.
Supervisor: Donkin, Stephen Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available