We characterise groups in which every abelian subgroup has finite index in its characteristic closure. In a group with this property every subgroup H has finite index in its characteristic closure and there is an upper bound for this index over all subgroups H of G. For every prime p we construct groups G with this property that are infinite nilpotent p-groups of class 2 and exponent p^2 in which G' = Z(G) is finite and Aut G acts trivially on G/G'. We also characterise abelian groups with the dual property that every subgroup has finite index over its characteristic core.

Finiteness conditions on characteristic closures and cores of subgroups / Cutolo, Giovanni; H., Smith; J., Wiegold. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - STAMPA. - 12:(2009), pp. 591-610. [10.1515/JGT.2008.092]

Finiteness conditions on characteristic closures and cores of subgroups

CUTOLO, GIOVANNI;
2009

Abstract

We characterise groups in which every abelian subgroup has finite index in its characteristic closure. In a group with this property every subgroup H has finite index in its characteristic closure and there is an upper bound for this index over all subgroups H of G. For every prime p we construct groups G with this property that are infinite nilpotent p-groups of class 2 and exponent p^2 in which G' = Z(G) is finite and Aut G acts trivially on G/G'. We also characterise abelian groups with the dual property that every subgroup has finite index over its characteristic core.
2009
Finiteness conditions on characteristic closures and cores of subgroups / Cutolo, Giovanni; H., Smith; J., Wiegold. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - STAMPA. - 12:(2009), pp. 591-610. [10.1515/JGT.2008.092]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/301140
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 4
social impact