We show that if w is a multilinear commutator word and G a finite group in which every metanilpotent subgroup generated by w-values is of rank at most r, then the rank of the verbal subgroup is bounded in terms of r and w only. In the case where G is soluble, we obtain a better result: if G is a finite soluble group in which every nilpotent subgroup generated by w-values is of rank at most r, then the rank of is at most.
On the rank of a verbal subgroup of a finite group
Detomi E.;
2022
Abstract
We show that if w is a multilinear commutator word and G a finite group in which every metanilpotent subgroup generated by w-values is of rank at most r, then the rank of the verbal subgroup is bounded in terms of r and w only. In the case where G is soluble, we obtain a better result: if G is a finite soluble group in which every nilpotent subgroup generated by w-values is of rank at most r, then the rank of is at most.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
2022-on-the-rank-of-a-verbal-subgroup-of-a-finite-group.pdf
accesso aperto
Tipologia:
Published (publisher's version)
Licenza:
Creative commons
Dimensione
468.68 kB
Formato
Adobe PDF
|
468.68 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
