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Some generalisations of Schur's and Baer's theorem and their connection with homological algebra

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  • Guram Donadze
  • Xabier García‐Martínez

Abstract

Schur's theorem and its generalisation, Baer's theorem, are distinguished results in group theory, connecting the upper central quotients with the lower central series. The aim of this paper is to generalise these results in two different directions, using novel methods related with the non‐abelian tensor product. In particular, we prove a version of Schur–Baer theorem for finitely generated groups. Then, we apply these newly obtained results to describe the k‐nilpotent multiplier, for k≥2, and other invariants of groups.

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  • Guram Donadze & Xabier García‐Martínez, 2021. "Some generalisations of Schur's and Baer's theorem and their connection with homological algebra," Mathematische Nachrichten, Wiley Blackwell, vol. 294(11), pages 2129-2139, November.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:11:p:2129-2139
    DOI: 10.1002/mana.201900495
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