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Generalized Grigorchuk’s overgroups as points in the space of marked 8-generated groups
Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2020-12-29 , DOI: 10.1142/s021949882250058x Supun T. Samarakoon 1
Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2020-12-29 , DOI: 10.1142/s021949882250058x Supun T. Samarakoon 1
Affiliation
First Grigorchuk group 𝒢 and Grigorchuk’s overgroup 𝒢 ̃ , introduced in 1980, are self-similar branch groups with intermediate growth. In 1984, 𝒢 was used to construct the family of generalized Grigorchuk groups { G ω | ω ∈ { 0 , 1 , 2 } ℕ } , which has many remarkable properties. Following this construction, we generalize the Grigorchuk’s overgroup 𝒢 ̃ to the family { G ̃ ω | ω ∈ { 0 , 1 , 2 } ℕ } of generalized Grigorchuk’s overgroups. We consider these groups as 8-generated and describe the closure of this family in the space ℳ 8 of marked 8 -generated groups.
中文翻译:
将 Grigorchuk 的过群概括为标记的 8 个生成群空间中的点
第一格里高丘克集团𝒢 和 Grigorchuk 的超群𝒢 ̃ ,于 1980 年引入,是具有中等增长的自相似分支组。1984 年,𝒢 用于构建广义 Grigorchuk 群的族{ G ω | ω ∈ { 0 , 1 , 2 } ℕ } , 它有许多显着的性质。按照这个结构,我们概括了 Grigorchuk 的超群𝒢 ̃ 给家人{ G ̃ ω | ω ∈ { 0 , 1 , 2 } ℕ } 广义 Grigorchuk 的超群。我们将这些组视为 8 生成并描述该家族在空间中的闭合ℳ 8 标记的8 - 生成的组。
更新日期:2020-12-29
中文翻译:
将 Grigorchuk 的过群概括为标记的 8 个生成群空间中的点
第一格里高丘克集团