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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

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Volume 14, Issue 4


Persistent homology of groups

Graham Ellis / Simon King
Published Online: 2010-12-01 | DOI: https://doi.org/10.1515/jgt.2010.064


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.

About the article

Received: 2010-07-31

Revised: 2010-09-01

Published Online: 2010-12-01

Published in Print: 2011-07-01

Citation Information: Journal of Group Theory, Volume 14, Issue 4, Pages 575–587, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt.2010.064.

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