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Transactions of the American Mathematical Society

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Cohomology of uniserial $ p$-adic space groups


Authors: Antonio Díaz Ramos, Oihana Garaialde Ocaña and Jon González-Sánchez
Journal: Trans. Amer. Math. Soc. 369 (2017), 6725-6750
MSC (2010): Primary 20J06, 55T10
DOI: https://doi.org/10.1090/tran/7145
Published electronically: May 5, 2017
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Abstract: A decade ago, J. F. Carlson proved that there are finitely many cohomology rings of finite $ 2$-groups of fixed coclass, and he conjectured that this result ought to be true for odd primes. In this paper, we prove the non-twisted case of Carlson's conjecture for any prime and we show how to proceed in the twisted case.


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Antonio Díaz Ramos
Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Apdo correos 59, 29080 Málaga, Spain
Email: adiazramos@uma.es

Oihana Garaialde Ocaña
Affiliation: Matematika Saila, Euskal Herriko Unibertsitatearen Zientzia eta Teknologia Fakultatea, posta-kutxa 644, 48080 Bilbao, Spain
Email: oihana.garayalde@ehu.es

Jon González-Sánchez
Affiliation: Departamento de Matemáticas, Facultad de Ciencia y Tecnología de la Universidad del Pais Vasco, Apdo correos 644, 48080 Bilbao, Spain
Email: jon.gonzalez@ehu.es

DOI: https://doi.org/10.1090/tran/7145
Received by editor(s): May 10, 2016
Received by editor(s) in revised form: October 12, 2016
Published electronically: May 5, 2017
Additional Notes: The first author was supported by MICINN grant RYC-2010-05663 and partially supported by MEC grant MTM2013-41768-P and Junta de Andalucía grant FQM-213
The second author was supported by the Basque Government Ph.D. grant PRE_2015_2_0130 and partially supported by the Spanish Ministry of Economy and Competitivity grant MTM2014-53810-C2-2-P and by the Basque Government grants IT753-13 and IT974-16
The third author acknowledges the support of grants MTM2011-28229-C02-01 and MTM2014-53810-C2-2-P from the Spanish Ministry of Economy and Competitivity, the Ramon y Cajal Programme of the Spanish Ministry of Science and Innovation, grant RYC-2011-08885, and of the Basque Government, grants IT753-13 and IT974-16
Article copyright: © Copyright 2017 American Mathematical Society

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