1 citations · 3 across the 6 of their papers we have counts for
7 papers
Profinite rigidity for free-by-cyclic groups with centre
Martin R. Bridson, Paweł Piwek
A free-by-cyclic group has non-trivial centre if and only if has finite order in . We establish a profinite ridigity result for such…
Solvable and non-solvable finite groups of the same order type
Paweł Piwek
We construct two finite groups of size : a solvable group and a non-solvable group , such that for every integer the groups have the s…
Lack of profinite rigidity among extensions with free quotient
Paweł Piwek
We present a construction that yields infinite families of non-isomorphic semidirect products sharing a specified profinite completion. Within each family, $m \ge 2…
Exact Count of Boundary Pieces of ReLU Classifiers: Towards the Proper Complexity Measure for Classification
Paweł Piwek, Adam Klukowski, Tianyang Hu
Classic learning theory suggests that proper regularization is the key to good generalization and robustness. In classification, current training schemes only target the complexity…
Profinite rigidity properties of central extensions of 2-orbifold groups
Paweł Piwek
We extend Wilkes' results on the profinite rigidity of SFSs to the setting of central extensions of 2-orbifold groups with higher-rank centre. We prove that both rigid and non-rigi…
Investigating transversals as generating sets for groups
Maurice Chiodo, Robert Crumplin, Oscar Donlan +1
In [3] is was shown that for any group whose rank (i.e., minimal number of generators) is at most 3, and any finite index subgroup with index , one…
Distinguishing crystallographic groups by their finite quotients
Paweł Piwek, David Popović, Gareth Wilkes
Using the computer algebra program GAP, we show that all crystallographic groups in dimensions at most 4 are distinguished from each other by their sets of finite quotients.