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Abstract: We introduce and investigate notions of persistent homology for p-groups andfor coclass trees of p-groups. Using computer techniques we show thatpersistent homology provides fairly strong homological invariants for p-groupsof order at most 81. The strength of these invariants, and some elementarytheoretical properties, suggest that persistent homology may be a useful toolin the study of prime-power groups.

Author: Graham Ellis, Simon A. King


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