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;
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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/301140
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