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Groups with boundedly many commutator of maximal order

Gunnar Traustason, Mercede Maj, Patrizia Longobardi, Pavel Shumyatsky

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/4519fe16-a86b-4275-9140-cdd9619668b7 • DOI: https://doi.org/10.1016/j.jalgebra.2020.09.011

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Abstract

By a result of Cocke and Venkataraman we know that if G is a group with at most m elements of maximal order, then is m-bounded. In this paper we consider the following related setting. Suppose G is a group with at most m commutators whose order is maximal among all commutators. What can we say about the structure of the group G?