Given a group-word w and a group G, the verbal subgroup w(G) is the one generated by all w-values in G. The word w is said to be boundedly concise if for each positive integer m there exists a number depending only on m and w bounding the order of w(G) whenever the set of w-values in a group G has size at most m. In the present article we show that various generalizations of the Engel word are boundedly concise in residually finite groups.
On bounded conciseness of Engel-like words in residually finite groups / Detomi E.; Morigi M.; Shumyatsky P.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 521:(2019), pp. 1-15. [10.1016/j.jalgebra.2018.11.020]
On bounded conciseness of Engel-like words in residually finite groups
Morigi M.;
2019
Abstract
Given a group-word w and a group G, the verbal subgroup w(G) is the one generated by all w-values in G. The word w is said to be boundedly concise if for each positive integer m there exists a number depending only on m and w bounding the order of w(G) whenever the set of w-values in a group G has size at most m. In the present article we show that various generalizations of the Engel word are boundedly concise in residually finite groups.| File | Dimensione | Formato | |
|---|---|---|---|
|
DMS_bounded_conciseness_revised.pdf
accesso aperto
Tipo:
Postprint
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione
463.67 kB
Formato
Adobe PDF
|
463.67 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
