Holomorphic reflexivity for locally finite and profinite groups: the abelian and general cases

Akbarov's theory of holomorphic reflexivity for topological Hopf algebras has been developed in two directions, namely, by the complication of definitions when expanding the scope and by their simplification when restricting. In the framework of the latter approach, we establish the holomorphic reflexivity for topological Hopf algebras associated with locally finite countable groups and second-countable profinite groups. In the Abelian case, the reflexivity is described in terms close to the classical ones.