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Strongly Indecomposable Butler Groups

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Abstract

We introduce a new class of torsion-free abelian groups which are special epimorphic images of finite rank completely decomposable groups. They belong to the well-known class of Butler groups by their definition. In comparison with the existing results the presented groups are not only of the maximal possible rank that is obviously less than the rank of the pre-image. The kernel of the above epimorphism admits a special matrix representation. The number of matrix rows is equal to the kernel rank and the number of its columns coincides with the preimage rank. By finitely many suitable operations the original matrix representation can be deduced to a special trapezoid form which corresponds to another choice of the epimorphism kernel generators. This matrix form clarifies the properties of the image that is exactly a group under investigation.

For this class of torsion-free abelian groups of finite rank a strong indecomposability criterion is proved on the basis of their matrix representation.

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Funding

The author is grateful to the German Academic Exchange Service (DAAD) for their support of this research. This work is supported by the Russian Foundation for Basic Research (project 20-01-00610).

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Authors and Affiliations

  1. Emperor Alexander I St. Petersburg State Transport University, 190031, St. Petersburg, Russia

    E. Blagoveshchenskaya

  2. Alferov Saint-Petersburg National Research Academic University, 190021, St. Petersburg, Russia

    E. Blagoveshchenskaya

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  1. E. Blagoveshchenskaya
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Correspondence to E. Blagoveshchenskaya.

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(Submitted byM. M. Arslanov)

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Blagoveshchenskaya, E. Strongly Indecomposable Butler Groups. Lobachevskii J Math 42, 709–715 (2021). https://doi.org/10.1134/S1995080221040077

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  • DOI: https://doi.org/10.1134/S1995080221040077

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