Speaker: Renu Joshi (Braunschweig)
Title: Combinatorial Invariants for Certain Classes of Non-Abelian Groups
Abstract:
In this talk, we explore several zero-sum invariants for a finite group \(G\): the small Davenport constant \(d(G)\), the ordered Davenport constant \(Dₒ(G)\), and the Loewy length \(L(G)\). We show that \(Dₒ(G) = d(G) + 1 = d(A) + 2\) for every non-abelian group of the form \(G = A ⋊₋₁ C₂\), where \(A\) is any finite abelian group. In addition, Dimitrov conjectured in 2004 that \(Dₒ(G) = L(G)\) for every finite non-abelian \(p\)-group \(G\). We provide explicit families of finite non-abelian \(p\)-groups for which Dimitrov’s conjecture holds.