We show that if all proper subgroups of a locally graded group G are finite-by-abelian-by-finite, then G contains a finite normal subgroup N such that all proper subgroups of G/N are abelian-by-finite. Then we apply this result to the study of groups which are minimal-non-P also for related group properties P. Finally we see how for locally (soluble-by-finite) groups of infinite rank, it is enough to restrict attention to the proper subgroups with infinite rank.
On groups with all proper subgroups finite-by-abelian-by-finite / Dardano, U.; De Mari, F.. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - 116:6(2021), pp. 611-619. [10.1007/s00013-021-01580-6]
On groups with all proper subgroups finite-by-abelian-by-finite
Dardano U.;De Mari F.
2021
Abstract
We show that if all proper subgroups of a locally graded group G are finite-by-abelian-by-finite, then G contains a finite normal subgroup N such that all proper subgroups of G/N are abelian-by-finite. Then we apply this result to the study of groups which are minimal-non-P also for related group properties P. Finally we see how for locally (soluble-by-finite) groups of infinite rank, it is enough to restrict attention to the proper subgroups with infinite rank.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.