Geodesic
Relative $B$-Groups
Documenta mathematica, Tome 24 (2019), pp. 2431-2462
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This paper extends the notion of B-group to a relative context. For a finite group K and a field F of characteristic 0, the lattice of ideals of the Green biset functor FBK​ obtained by shifting the Burnside functor FB by K is described in terms of BK​-groups. It is shown that any finite group (L,φ) over K admits a largest quotient BK​-group βK​(L,φ). The simple subquotients of FBK​ are parametrized by BK​-groups, and their evaluations can be precisely determined. Finally, when p is a prime, the restriction FBK(p)​ of FBK​ to finite p-groups is considered, and the structure of the lattice of ideals of the Green functor FBK(p)​ is described in full detail. In particular, it is shown that this lattice is always finite.
DOI : 10.4171/dm/730
Classification : 18B99, 19A22, 20J15
Mots-clés : Burnside ring, B-group, biset functor, shifted functor 
@article{10_4171_dm_730,
     author = {Serge Bouc},
     title = {Relative $B${-Groups}},
     journal = {Documenta mathematica},
     pages = {2431--2462},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/730},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/730/}
}
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Serge Bouc. Relative $B$-Groups. Documenta mathematica, Tome 24 (2019), pp. 2431-2462. doi: 10.4171/dm/730

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