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math.GR2026
Streaming algorithms for groups and semigroups
Markus Lohrey, Lukas Lück, Alexander Thumm +1
We investigate deterministic and randomized streaming algorithms for word problems in finitely generated groups and semigroups. For this we introduce the notion of a distinguisher:…
math.GR2026
Quadratic Equations in Graph Products of Groups and the Exponent of Periodicity
Volker Diekert, Silas Natterer, Alexander Thumm
In 1977, Makanin established the decidability of equations in free monoids. A key ingredient in his proof is the exponent of periodicity: for a word , it is the largest exponent…
math.GR2025
Finite groups with geodetic Cayley graphs
Murray Elder, Adam Piggott, Florian Stober +2
A connected undirected graph is called \emph{geodetic} if for every pair of vertices there is a unique shortest path connecting them. It has been conjectured that for finite groups…