A characterization of finite modular 2-groups via magnitude homology

Finite quasihamiltonian groups - that is, finite groups in which every pair of subgroups commutes - admit several characterizations. In this work, after introducing the notion of sectional contractibility graph, we provide a new characterization in terms of (a suitable subgroup of) magnitude homology. Our approach especially focuses on the subgroup lattices of finite groups and on the related notion of modularity. We present a detailed study for finite 2-groups, and, in particular, in the case of extraspecial 2-groups and Pauli groups. These groups, of interest because of their diverse applications in both mathematics and physics, already describe the wealth of information that one can obtain in restricting the study to the case of 2-groups.