The aim of this paper is to investigate the behaviour of projective images of the groups which are finite over a term of their upper central series. In particular, we prove that for any positive integer k, the class of finitely generated groups in which the k-th term of the upper central series has finite index can be described in terms of lattice invariants, and so it is invariant under projectivities. In this context, we also study groups that have only finitely many maximal subgroups which are not permodular.
Modular chains in infinite groups / De Falco, M.; de Giovanni, F.; Musella, C.. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - 117:(2021), pp. 601-612. [10.1007/s00013-021-01665-2]
Modular chains in infinite groups
M. De Falco;F. de Giovanni;C. Musella
2021
Abstract
The aim of this paper is to investigate the behaviour of projective images of the groups which are finite over a term of their upper central series. In particular, we prove that for any positive integer k, the class of finitely generated groups in which the k-th term of the upper central series has finite index can be described in terms of lattice invariants, and so it is invariant under projectivities. In this context, we also study groups that have only finitely many maximal subgroups which are not permodular.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
