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math.GR2025
Characteristic Subgroup Growth
Liam Hanany, Alexander Lubotzky
Let denote the number of characteristic subgroups of index at most in a finitely generated group . In response to a question of I. Rivin we show that if…
math.GR2025
The Yang-Baxter Equation and Characteristic Finite Simple Quotients of the Free Group of Rank
Liam Hanany
We show that infinitely many alternating groups arise as quotients of the free group of rank 2, with kernel a characteristic subgroup. We also show that such simple quotients exist…
math.GR2025
Non-uniform higher-rank lattices are character rigid
Alon Dogon, Michael Glasner, Yuval Gorfine +2
We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for proba…