On uniformly fully inert subgroups of abelian groups

Abstract

If H is a subgroup of an abelian group G and φ ∈ End(G), H is called φ-inert (and φ is H-inertial) if φ(H) ∩ H has finite index in the image φ(H). The notion of φ-inert subgroup arose and was investigated in a relevant way in the study of the so called intrinsic entropy of an endomorphism φ, while inertial endo-morphisms (these are endomorphisms that are H-inertial for every subgroup H) were intensively studied by Rinauro and the first named author.

Keywords

• fully invariant subgroup
• φ-inert subgroup
• fully inert subgroup
• uniformly fully inert subgroup
• commensurable subgroup
• primary: 20k27, 20k30
• secondary: 20k15, 20k21