Piotr Grzeszczuk

activity

20192026

collaborators

5 papers

math.CO2026

Colouring bijections of finite $3$ -groups

Piotr Grzeszczuk

Let $G$ be a finite group. A bijection $σ : G \to G$ is a \emph{colouring bijection} if the three maps \[ Δ^{+}\colon x\mapsto x\,σ(x), \qquad Δ^{-}\colon x\mapsto x^{-1}σ(x), \…

math.RA2020

Locally nilpotent skew extensions of rings

Piotr Grzeszczuk

We extend existing results on locally nilpotent differential polynomial rings to skew extensions of rings. We prove that if $G = {σ_{t}}_{t \in T}$ is a locally finite famil…

math.CO2019

On the generic family of Cayley graphs of a finite group

Czesław Bagiński, Piotr Grzeszczuk

Let $G$ be a finite group. For each $m > 1$ we define the symmetric canonical subset $S = S (m)$ of the Cartesian power $G^{m}$ and we consider the family of Cayley graphs $\mathscr{G}_m(…

math.RA2019

On the semiprimitivity of free skew extensions of rings

Jeffrey Bergen, Piotr Grzeszczuk

Let $X$ be a set of noncommuting variables of cardinality $c a r d (X) ⩾ 2$ , and $G = {σ_{x}}_{x \in X}$ , $D = {δ_{x}}_{x \in X}$ be families of automorphisms an…

math.RA2019

Generic identities for finite group actions

Piotr Grzeszczuk

Let $G$ be a finite group of order $n$ , and $Z_{G} = Z ⟨ ζ_{i, g} ∣ g \in G, i = 1, 2, \dots, n ⟩$ be the free generic algebra, with canonical action of $G$ according to…

Colouring bijections of finite 3-groups

Locally nilpotent skew extensions of rings

On the generic family of Cayley graphs of a finite group

On the semiprimitivity of free skew extensions of rings

Generic identities for finite group actions

Colouring bijections of finite $3$ -groups