一个无限有限呈现周期群
An infinite finitely presented periodic group
OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。
具体内容
稿件研究有限呈现Burnside问题及相关代数结构。作者声称构造一个具有普通有限呈现且每个元素阶有限的无限群，从而否定有限呈现Burnside问题；还构造𝔽2上无限维有限呈现非单位零结合代数，为Jacobson根但非幂零，其单位化有限呈现、代数且无限维。摘要称这些代数否定有限呈现零代数与根代数幂零问题及Kurosh代数有限性问题的有限呈现版本。手稿为AI产生，未经独立审查或同行评议。
- 构造无限、有限呈现且每元素有限阶的群，否定有限呈现Burnside问题
- 构造𝔽2上无限维有限呈现非单位零结合代数，Jacobson根但非幂零
- 作者声称这些结果否定若干有限呈现版本的代数幂零与有限性问题
AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。
英文原始摘要
We construct an infinite group with an ordinary finite presentation in which every element has finite order, answering the finitely presented Burnside question negatively. We also construct an infinite-dimensional finitely presented nonunital nil associative algebra over 𝔽2 that is Jacobson radical but not nilpotent. Its unitization is finitely presented, algebraic, and infinite-dimensional. These algebras answer the finitely presented nil- and radical-algebra nilpotence questions and the finite-presentation version of Kurosh's algebraic finiteness question negatively.
用户标记：未标记
固定编号：b5aecb828f2db722
原文来源