On weak Sierpinski subsets in groups

Abstract: A subset $E$ in a group $G$ is called a weak Sierpinski subset if for some $g, h$ in $G$ and $a$ different from $b$ in $E$, we have $gE = E \setminus \{a\}$ and $hE = E \setminus \{b\}$. In the talk we discuss the subgroup generated by $g$ and $h$, and show that either it is free over $(g,h)$ or it has presentation $G(k)=\left\langle g, h \mid (h^{-1}g)^k \right\rangle$. We also characterize all weak Sierpinski subsets in the groups $G(k)$. This is joint work with Y. Cornulier and P. Slanina.

group theory

Audience: researchers in the topic

GOThIC - Ischia Online Group Theory Conference

Series comments: Please send a message to andrea.caranti@unitn.it to receive a link to the Zoom room where the conference (a series of talks, actually) takes place.