It is proved that if G is a (generalized) soluble group of infinite rank in which all proper subgroups of infinite rank are permodular, then the subgroup lattice of G is permodular. As a consequence of this theorem, we obtain shorter proofs for corresponding known results concerning normal or permutable subgroups of groups of infinite rank.
A note on groups of infinite rank with modular subgroup lattice / DE FALCO, Maria; DE GIOVANNI, Francesco; Musella, Carmela. - In: MONATSHEFTE FÜR MATHEMATIK. - ISSN 0026-9255. - 176:(2015), pp. 81-86. [10.1007/S00605-014-0610-X]
A note on groups of infinite rank with modular subgroup lattice
DE FALCO, MARIA;DE GIOVANNI, FRANCESCO;MUSELLA, CARMELA
2015
Abstract
It is proved that if G is a (generalized) soluble group of infinite rank in which all proper subgroups of infinite rank are permodular, then the subgroup lattice of G is permodular. As a consequence of this theorem, we obtain shorter proofs for corresponding known results concerning normal or permutable subgroups of groups of infinite rank.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Falco2015_Article_ANoteOnGroupsOfInfiniteRankWit.pdf
solo utenti autorizzati
Tipologia:
Versione Editoriale (PDF)
Licenza:
Accesso privato/ristretto
Dimensione
110.88 kB
Formato
Adobe PDF
|
110.88 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
