It is known that if G is a group such that the centre factor group G/ ζ(G) is polycyclic, then also the commutator subgroup G′ is polycyclic. The aim of this paper is to describe this situation from a lattice point of view. It is proved that if G is a group admitting a permodularly embedded non-periodic subgroup P such that the interval [G/P] is a polycyclic lattice, then G contains a polycyclic normal subgroup N such that G/N is quasihamiltonian.
A note on groups with a large permodularly embedded subgroup / De Falco, M.; de Giovanni, F.; Musella, C.. - In: BEITRAGE ZUR ALGEBRA UND GEOMETRIE. - ISSN 0138-4821. - 65:2(2024), pp. 441-449. [10.1007/s13366-023-00699-7]
A note on groups with a large permodularly embedded subgroup
De Falco M.;de Giovanni F.
;Musella C.
2024
Abstract
It is known that if G is a group such that the centre factor group G/ ζ(G) is polycyclic, then also the commutator subgroup G′ is polycyclic. The aim of this paper is to describe this situation from a lattice point of view. It is proved that if G is a group admitting a permodularly embedded non-periodic subgroup P such that the interval [G/P] is a polycyclic lattice, then G contains a polycyclic normal subgroup N such that G/N is quasihamiltonian.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
