We give a complete classification of all d-representation-finite symmetric Nakayama algebras and of all d-representation-finite trivial extensions of path algebras of quivers, over an arbitrary field. As a consequence, we get a classification, up to Morita equivalence, of all d-representation-finite symmetric algebras of finite representation type over an algebraically closed field.
Recently, Kim and Lee [9] presented an example of a non-Hopfian relatively hyperbolic group with a Hopfian peripheral subgroup, demonstrating a counterexample to Osin's well-known question [12, Problem 5.5]. In this paper, we provide a general construction method using the so-called image extension theorem to generate non-Hopfian relatively hyperbolic groups with Hopfian peripheral subgroups. Additionally, we provide two specific examples using this construction method.
