Publications

On the class-breadth conjecture for algebras and T-groups.

With Bettina Eick.

Submitted, 2025.

We describe an algorithm to compute the breadth of an algebra given by structure constants and show how this can be used to compute the breadth of a finitely generated torsion-free nilpotent group. We give a new proof that the class-breadth conjecture holds in finite-dimensional nilpotent algebras over infinite fields and in finitely generated torsion-free nilpotent groups.

The conjugacy problem and canonical representatives in finitely generated nilpotent groups.

With Bettina Eick.

Journal of Symbolic Computation. Vol 130, 2025, DOI.

We describe algorithms that determine a canonical representative of a conjugacy class of elements, lists and subgroups in finitely generated nilpotent groups. The algorithms thus solve the associated conjugacy problems. They additionally compute the corresponding centralizers or normalizers, respectively.