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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cohomological uniqueness, Massey products and the modular isomorphism problem for $ 2$-groups of maximal nilpotency class


Authors: Albert Ruiz and Antonio Viruel
Journal: Trans. Amer. Math. Soc. 365 (2013), 3729-3751
MSC (2010): Primary 55R35, 20D15
Published electronically: January 24, 2013
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Abstract: Let $ G$ be a finite $ 2$-group of maximal nilpotency class, and let $ BG$ be its classifying space. We prove that iterated Massey products in $ H^*(BG;\mathbb{F}_2)$ do characterize the homotopy type of $ BG$ among $ 2$-complete spaces with the same cohomological structure. As a consequence we get an alternative proof of the modular isomorphism problem for $ 2$-groups of maximal nilpotency class.


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Additional Information

Albert Ruiz
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Vallès, Spain
Email: Albert.Ruiz@uab.cat

Antonio Viruel
Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Apdo correos 59, 29080 Málaga, Spain
Email: viruel@agt.cie.uma.es

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05756-X
PII: S 0002-9947(2013)05756-X
Received by editor(s): April 29, 2011
Received by editor(s) in revised form: November 3, 2011
Published electronically: January 24, 2013
Additional Notes: The first author was partially supported by FEDER-MEC grant MTM2010-20692
The second author was partially supported by FEDER-MEC grant MTM2010-18089 and Junta de Andalucía grants FQM-213 and P07-FQM-2863
Both authors were partially supported by Generalitat de Catalunya grant 2009SGR-1092.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.