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On the cokernel of the Baumslag rationalization

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Abstract

We prove that for the free group of rank two F the cokernel of the homomorphism to its Baumslag rationalization F → Bau(F) is not abelian. Moreover, this cokernel contains a free subgroup of countable rank. This answers a question of Emmanuel Farjoun.

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Authors and Affiliations

  1. Laboratory of Modern Algebra and Applications, St. Petersburg State University, 14th Line, 29b, Saint Petersburg, 199178, Russia

    Sergei O. Ivanov

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  1. Sergei O. Ivanov
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Correspondence to Sergei O. Ivanov.

Additional information

The work is supported by: (1) Ministry of Science and Higher Education of the Russian Federation, agreement 075-15-2019-1619; (2) the grant of the Government of the Russian Federation for the state support of scientific research carried out under the supervision of leading scientists, agreement 14.W03.31.0030 dated 15.02.2018; (3) RFBR according to the research project 20-01-00030; (4) Russian Federation President Grant for Support of Young Scientists MK-681.2020.1.

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Ivanov, S.O. On the cokernel of the Baumslag rationalization. Isr. J. Math. 253, 407–418 (2023). https://doi.org/10.1007/s11856-022-2369-4

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  • DOI: https://doi.org/10.1007/s11856-022-2369-4

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