Takuya Sakasai

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math.GR2025

The spherical growth series of amalgamated free products of infinite cyclic groups

Michihiko Fujii, Takuya Sakasai

Let $n$ be an integer greater than $1$ . We consider a group presented as $G (p_{1}, p_{2}, \dots, p_{n}) = ⟨ x_{1}, x_{2}, \dots, x_{n} ∣ x_{1}^{p_{1}} = x_{2}^{p_{2}} = \dots = x_{n}^{p_{n}} ⟩$ , with…

math.GR2025

On the structure of groups defined by Kim and Manturov

Carl-Fredrik Nyberg-Brodda, Takuya Sakasai, Yuuki Tadokoro +1

We study the structure of a series of groups $Γ_{n}^{4}$ defined by Kim and Manturov. We show that the groups are finite for all $n \geq 6$ and in fact they are 2-step nilpotent $2$ -gro…