Persistent homology of groups
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Ellis, Graham; King, Simon (2011). Persistent homology of groups. Journal of Group Theory 14 (4), 575-587
We introduce and investigate notions of persistent homology for p-groups and for coclass trees of p-groups. Using computer techniques we show that persistent homology provides fairly strong homological invariants for p-groups of order at most 81. The strength of these invariants, together with some of their elementary theoretical properties, suggest that persistent homology may be a useful tool in the study of prime-power groups. In particular, we ask whether the known periodic structure on coclass trees is reflected in a periodic structure on the persistent homology of p-groups in the trees.