Elementary Theory of Groups and Group Rings, and Related Topics: Proceedings of the Conference held at Fairfield University and at the Graduate ... 2018 (De Gruyter Proceedings in Mathematics)

This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments. Introduction Conference booklet and talks Remembrances of Gilbert Contents Explicit universal axioms for Kaplansky groups Isoperimetric and isodiametric functions of group extensions The homology of groups, profinite completions, and echoes of Gilbert Baumslag Some properties of the Baumslag groups G(m, n) Some model theory of the Heisenberg group: I. Unitriangular representations of models of a subtheory of its universal theory Some model theory of the Heisenberg group: II. The three generator case On vector-valued Hecke forms Two algorithms in group theory On products of closed subsets in free groups Misbehaved direct products A survey on Albert algebras and groups of type F 4 Perspectives on p-ary bent functions Multilinear cryptography using nilpotent groups Musings on generic-case complexity Noncommutative Gebauer–Möller criteria On the numbers of the form x 2 + 11y 2 Separability properties of nilpotent Q[x]-powered groups Infinite nested radicals Commutative transitivity property in groups and Lie algebras Simplicial subdivisions and the chromatic number of a group