Homotopy types of group lattices
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In this article, we study group lattices using the ideas of K. S. Brown and D. Quillen of associating a certain topological space to a partially ordered set. We determine the exact homotopy type for the subgroup lattice of PSL(2, 7), find a connection between different group lattices, and obtain some estimates for the Betti numbers of these lattices using the spectral sequence method.
KeywordsTopological Space Conjugacy Class Spectral Sequence Simplicial Complex Maximal Element
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