Mathematical classification demonstrates contractibility of elementary abelian subgroup posets in specific finite 2-groups, clarifying topological properties of subgroup lattices.
Let p be an arbitrary prime number and let P be a finite p-group. Let Ap(P)≥2 be the poset of all elementary abelian subgroups of P of rank at least 2. Bouc and Thévenaz proved that Ap(P)≥2 has the homotopy type of a wedge of spheres (of possibly different dimensions). In this paper, we firstly classify finite 2-groups P with both cyclic center and P′≅C2×C2, then compute exactly the homotopy type of Ap(P)≥2 and prove that Ap(P)≥2 is contractible in this case.
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Fu et al. (2026) studied this question.
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