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.File in questo prodotto:
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