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, and some elementary
theoretical properties, suggest that persistent homology may be a useful tool
in the study of prime-power groups.Comment: 12 pages, 6 figure
