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Chains of modular elements and connectivity of order complexes of finite lattices

Giovedi 10 Giugno - prof. John Shareshian

ARGOMENTI: Seminari

Giovedi 10 Giugno alle ore 10.30 in aula 2AB/40 il prof. John Shareshian (Washington University) terra' un seminario dal titolo "Chains of modular elements and connectivity of order complexes of finite lattices".

-Abstract
Shareshian and Hersh observed that if a finite lattice L contains a chain 0=x_0<...<x_r=1 of modular elements then the order complex of L-{0,1} is (at least) (r-3)-connected. In this work, we show that this lower bound is tight if and only if there is a maximal chain 0=c_r<...<c_0=1 in L such that c_i is a complement to m_i for each i. We show also that no chain of modular elements in the subgroup lattice of a finite group can be longer than a chief series, and use this fact to show that, for a finite group G, the connectivity bound described above is tight if and only if G is solvable and every normal subgroup of G has a complement.

Venerdi 11 si terra' anche il seminario "Eulerian quasisymmetric functions".

Rif. int. A. Lucchini

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