We describe soluble groups in which the set of all subgroups is countable and show that locally (soluble-by-finite) groups with this property are soluble-by-finite. Further, we construct a nilpotent group with uncountably many subgroups in which the set of all abelian subgroups is countable.

Groups with countably many subgroups / Cutolo, Giovanni; Smith, Howard. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 448:(2016), pp. 399-417. [10.1016/j.jalgebra.2015.10.007]

Groups with countably many subgroups

CUTOLO, GIOVANNI;
2016

Abstract

We describe soluble groups in which the set of all subgroups is countable and show that locally (soluble-by-finite) groups with this property are soluble-by-finite. Further, we construct a nilpotent group with uncountably many subgroups in which the set of all abelian subgroups is countable.
2016
Groups with countably many subgroups / Cutolo, Giovanni; Smith, Howard. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 448:(2016), pp. 399-417. [10.1016/j.jalgebra.2015.10.007]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/681982
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