Ulm Function Analysis of Full Transitivity in Primary Abelian Groups
J. Tom Otobong, Eno John, M. Udo Udeme, Michael N. John ยท International Journal of Mathematics and Statistics Studies ยท 2024
This research addresses the problem posed by Chekhlov and Danchev (2015) regarding variations of Kaplansky's full transitivity in primary abelian groups ๐บ. By delving into three distinct forms of full transitivity within the endomorphism ring of ๐บ, specifically focusing on subgroups, subrings, and unitary subrings generated by commutator endomorphisms, we aim to provide a comprehensive understanding of the totally projective groups exhibiting these properties. The Ulm function of ๐บ emerges as a key tool in solving this problem and related inquiries, leading to a precise characterization of the groups involved.