Abstract
A well known theorem of R. Baer states that if G is a group and \(G/Z_{n}(G)\) is finite, then \( \gamma _{n+1}(G) \) is finite. In this article, we extend this theorem for groups G that have subgroups A of Aut(G) such that A/Inn(G) is finitely generated or is of finite special rank. Furthermore, some new upper bounds for \(|\gamma _{n+1}(G)| \) and \( |\gamma _{n+1}(G,A)| \) are presented.
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Taghavi, Y., Kayvanfar, S. & Parvizi, M. On Baer’s Theorem and Its Generalizations. Mediterr. J. Math. 18, 254 (2021). https://doi.org/10.1007/s00009-021-01887-2
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DOI: https://doi.org/10.1007/s00009-021-01887-2