The global dimension of rational incomplete Mackey functors for finite abelian groups is bounded via splitting results and exactly computed for disk-like cases using incidence algebras over posets.
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Explicit widths and complete lattices of G-transfer systems are given for dihedral, quaternion, dicyclic, Frobenius, and alternating groups.
w(SD_{2^n}) and w(AGL(1,p^n)) are computed explicitly, c(D_{p^n}) equals floor(3n/2)+1, and c(SD_{2^n}) is at least floor(5(n-1)/2).
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Global dimension of the category of rational incomplete Mackey functors for a finite abelian group G
The global dimension of rational incomplete Mackey functors for finite abelian groups is bounded via splitting results and exactly computed for disk-like cases using incidence algebras over posets.
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Characterizing Transfer Systems for Non-Abelian Groups
Explicit widths and complete lattices of G-transfer systems are given for dihedral, quaternion, dicyclic, Frobenius, and alternating groups.
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Minimal generating sets of transfer systems for more non-Abelian Groups
w(SD_{2^n}) and w(AGL(1,p^n)) are computed explicitly, c(D_{p^n}) equals floor(3n/2)+1, and c(SD_{2^n}) is at least floor(5(n-1)/2).