On finite groups with bounded conjugacy classes of commutators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915947577606144 |
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| author | Senise, Débora Shumyatsky, Pavel |
| author_facet | Senise, Débora Shumyatsky, Pavel |
| contents | In 1954 B. H. Neumann discovered that if $G$ is a group in which all conjugacy classes have finite cardinality at most $m$, then the derived group $G'$ is finite of $m$-bounded order. In 2018 G. Dierings and P. Shumyatsky showed that if $|x^G| \le m$ for any commutator $x\in G$, then the second derived group $G''$ is finite and has $m$-bounded order. This paper deals with finite groups in which $|x^G|\le m$ whenever $x\in G$ is a commutator of prime power order. The main result is that $G''$ has $m$-bounded order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On finite groups with bounded conjugacy classes of commutators Senise, Débora Shumyatsky, Pavel Group Theory In 1954 B. H. Neumann discovered that if $G$ is a group in which all conjugacy classes have finite cardinality at most $m$, then the derived group $G'$ is finite of $m$-bounded order. In 2018 G. Dierings and P. Shumyatsky showed that if $|x^G| \le m$ for any commutator $x\in G$, then the second derived group $G''$ is finite and has $m$-bounded order. This paper deals with finite groups in which $|x^G|\le m$ whenever $x\in G$ is a commutator of prime power order. The main result is that $G''$ has $m$-bounded order. |
| title | On finite groups with bounded conjugacy classes of commutators |
| topic | Group Theory |
| url | https://arxiv.org/abs/2502.04124 |