If G is an uncountable group of regular cardinality ℵ, we shall denote by LLℵ(G) the set of all subgroups of G of cardinality ℵ. The aim of this paper is to describe the behaviour of groups G for which the set Cℵ(G)={X′|X∈LLℵ(G)} is finite, at least when G is locally graded and has no simple sections of cardinality ℵ. Among other results, it is proved that such a group has a finite commutator subgroup, provided that it contains an abelian subgroup of cardinality ℵ.
A note on commutator subgroups in groups of large cardinality / De Falco, M.; de Giovanni, F.; Musella, C.. - In: MONATSHEFTE FÜR MATHEMATIK. - ISSN 0026-9255. - 191:2(2020), pp. 249-256. [10.1007/s00605-019-01302-9]
A note on commutator subgroups in groups of large cardinality
De Falco M.;de Giovanni F.;Musella C.
2020
Abstract
If G is an uncountable group of regular cardinality ℵ, we shall denote by LLℵ(G) the set of all subgroups of G of cardinality ℵ. The aim of this paper is to describe the behaviour of groups G for which the set Cℵ(G)={X′|X∈LLℵ(G)} is finite, at least when G is locally graded and has no simple sections of cardinality ℵ. Among other results, it is proved that such a group has a finite commutator subgroup, provided that it contains an abelian subgroup of cardinality ℵ.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
