Almost congruence extension property for subgroups of free groups Article uri icon

abstract

  • Let H be a subgroup of F and ((H))F the normal closure of H in F. We say that H has the Almost Congruence Extension Property (ACEP) in F if there is a finite set of nontrivial elements F ⊂ H such that for any normal subgroup N of H one has H ∩ ((N))F = N whenever N ∩ F = . In this paper, we provide a sufficient condition for a subgroup of a free group to not possess ACEP. It also shows that any finitely generated subgroup of a free group satisfies some generalization of ACEP. © de Gruyter 2018.

publication date

  • 2018-01-01