2013/10/17 by Ulderico Dardano, Dardano, Ulderico, Silvana Rinauro +1 · 1 citation
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #graph theory and CDMA systems #math.GR
paper · pdf · doi:10.48550/arxiv.1310.4625
arxiv created 2013/10/17 · openalex publication_date 2013/10/17 · arxiv updated 2013/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe inertial endomorphisms of an abelian group A, that is endomorphisms φ with the property |(φ(X)+X)/X|<∞ for each X≤ A. They form a ring containing multiplications, the so-called finitary endomorphisms and non-trivial instances. We show that inertial invertible endomorphisms form a group, provided A has finite torsion-free rank. In any case, the group IAut(A) they generate is commutative modulo the group FAut(A) of finitary automorphisms, which is known to be locally finite. We deduce that IAut(A) is locally-(center-by-finite). Also we consider the lattice dual property, that is that |X/(X∩ φ(X))|<∞ for each X≤ A. We show that this implies the above one, provided A has finite torsion-free rank.