Zobrazeno 1 - 8
of 8
pro vyhledávání: '"Piwek, Paweł"'
Autor:
Bridson, Martin R., Piwek, Paweł
A free-by-cyclic group $F_N\rtimes_\phi\mathbb{Z}$ has non-trivial centre if and only if $[\phi]$ has finite order in ${\rm{Out}}(F_N)$. We establish a profinite ridigity result for such groups: if $\Gamma_1$ is a free-by-cyclic group with non-trivia
Externí odkaz:
http://arxiv.org/abs/2409.20513
Autor:
Piwek, Paweł
We construct two finite groups of size $2^{365}\cdot 3^{105}\cdot 7^{104}$: a solvable group $G$ and a non-solvable group $H$, such that for every integer $n$ the groups have the same number of elements of order $n$. This answers a question posed in
Externí odkaz:
http://arxiv.org/abs/2403.02197
Classic learning theory suggests that proper regularization is the key to good generalization and robustness. In classification, current training schemes only target the complexity of the classifier itself, which can be misleading and ineffective. In
Externí odkaz:
http://arxiv.org/abs/2306.08805
Autor:
Piwek, Paweł
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-rigid phenomena arise in this setting and that the non-rigid phenomena are
Externí odkaz:
http://arxiv.org/abs/2304.01105
In [3] is was shown that for any group $G$ whose rank (i.e., minimal number of generators) is at most 3, and any finite index subgroup $H\leq G$ with index $[G:H]\geq rank(G)$, one can always find a left-right transversal of $H$ which generates $G$.
Externí odkaz:
http://arxiv.org/abs/1912.02717
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.
Comment: GAP code now included in ancillary files
Comment: GAP code now included in ancillary files
Externí odkaz:
http://arxiv.org/abs/1910.09845
Autor:
Piwek, Paweł
Publikováno v:
Transactions of the American Mathematical Society; Jan2025, Issue 1, p635-650, 16p
Publikováno v:
In Journal of Algebra 1 January 2021 565:548-563