Doron Shafrir

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20242026

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math.GR2024

Sections of Submonoids of Nilpotent Groups

Doron Shafrir

We show that every product of f.g.\ submonoids of a group $G$ is a section of a f.g.\ submonoid of $G \times H_{5} (Z)$ , where $H_{5} (Z)$ is a Heisenberg group. This g…

math.GR2024

Is decidability of the Submonoid Membership Problem closed under finite extensions?

Doron Shafrir

We show that the rational subset membership problem in $G$ can be reduced to the submonoid membership problem in $G \times H$ where $H$ is virtually Abelian. We use this to show th…

math.GR2024

Bounded Generation of Submonoids of Heisenberg Groups

Doron Shafrir

If $G$ is a nilpotent group and $[G, G]$ has Hirsch length $1$ , then every f.g. submonoid of $G$ is boundedly generated, i.e. a product of cyclic submonoids. Using a reduction of Bo…

math.GR2024

A saturation theorem for submonoids of nilpotent groups and the Identity Problem

Doron Shafrir

If $M$ is a submonoid of a finitely generated nilpotent group $G$ , and $M G^{'}$ is a finite index subgroup of $G$ , then $M$ itself is a finite index subgroup of $G$ . If $M G^{'} = G$ , then…