Commutator endomorphisms of totally projective abelian 𝑝-groups

Abstract

Abstract For a primary abelian group 𝐺, Chekhlov and Danchev (2015) defined three variations of Kaplansky’s notion of full transitivity by restricting one’s attention to the subgroup, the subring and the unitary subring of the endomorphism ring of 𝐺 generated by the collection of all commutator endomorphisms. They posed the problem of describing exactly which totally projective groups exhibit these forms of full transitivity. This problem, and some closely related questions, are completely answered using the Ulm function of 𝐺.