Profinite groups with restricted centralizers of powers
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908987613511680 |
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| author | Acciarri, Cristina Shumyatsky, Pavel |
| author_facet | Acciarri, Cristina Shumyatsky, Pavel |
| contents | A group $G$ is said to have restricted centralizers if for every $x\in G$ the centralizer $C_G(x)$ either is finite or has finite index in $G$. Shalev showed that a profinite group with restricted centralizers is virtually abelian. Here we take interest in profinite groups $G$ for which there is an integer $n$ such that $C_G(x^n)$ is either finite or open whenever $x\in G$. It is shown that such a group $G$ has an open normal subgroup $T$ with the property that $G/Z(T)$ has finite exponent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18839 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Profinite groups with restricted centralizers of powers Acciarri, Cristina Shumyatsky, Pavel Group Theory 20E18, 20F24 A group $G$ is said to have restricted centralizers if for every $x\in G$ the centralizer $C_G(x)$ either is finite or has finite index in $G$. Shalev showed that a profinite group with restricted centralizers is virtually abelian. Here we take interest in profinite groups $G$ for which there is an integer $n$ such that $C_G(x^n)$ is either finite or open whenever $x\in G$. It is shown that such a group $G$ has an open normal subgroup $T$ with the property that $G/Z(T)$ has finite exponent. |
| title | Profinite groups with restricted centralizers of powers |
| topic | Group Theory 20E18, 20F24 |
| url | https://arxiv.org/abs/2602.18839 |