3 papers
math.GR2025
Hereditarily and Super Generalized co-Bassian Abelian Groups
Peter V. Danchev, Brendan Goldsmith, Patrick W. Keef
We completely characterize by finding necessary and sufficient conditions those co-Bassian and generalized co-Bassian Abelian groups having, respectively, the hereditary or the sup…
math.GR2025
On Some Hereditary and Super Classes of Directly Finite Abelian Groups
Peter Danchev, Brendan Goldsmith, Fatemeh Karimi
Continuing recent studies of both the hereditary and super properties of certain classes of Abelian groups, we explore in-depth what is the situation in the quite large class consi…
math.GR2024
Two Generalizations of Hopfian Abelian Groups
Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith +1
This paper targets to generalize the notion of Hopfian groups in the commutative case by defining the so-called {\bf relatively Hopfian groups} and {\bf weakly Hopfian groups}, and…