Persistent homology of groups
Graham J. Ellis, Simon King · Journal of Group Theory · 2010
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.