Abstract
If G is an uncountable group of regular cardinality \(\aleph \), we shall denote by \({\mathfrak {L}L}_\aleph (G)\) the set of all subgroups of G of cardinality \(\aleph \). The aim of this paper is to describe the behaviour of groups G for which the set \({{\mathcal {C}}}_\aleph (G)=\{ X'\;|\; X\in {\mathfrak {L}L}_\aleph (G)\}\) is finite, at least when G is locally graded and has no simple sections of cardinality \(\aleph \). Among other results, it is proved that such a group has a finite commutator subgroup, provided that it contains an abelian subgroup of cardinality \(\aleph \).
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Communicated by A. Constantin.
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De Falco, M., de Giovanni, F. & Musella, C. A note on commutator subgroups in groups of large cardinality. Monatsh Math 191, 249–256 (2020). https://doi.org/10.1007/s00605-019-01302-9
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DOI: https://doi.org/10.1007/s00605-019-01302-9