Normal subgroups of non-torsion multi-EGS groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914031388852224 |
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| author | Klopsch, Benjamin Thillaisundaram, Anitha |
| author_facet | Klopsch, Benjamin Thillaisundaram, Anitha |
| contents | We study the distribution of normal subgroups in non-torsion, regular branch multi-EGS groups and show that the congruence completions of such groups have bounded finite central width. In particular, we show that the profinite completion of the Fabrykowski--Gupta group acting on the $p$-adic tree has central width 2 for every odd prime $p$. The methods used also apply to the family of Sunic groups, which closely resemble the Grigorchuk group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08576 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normal subgroups of non-torsion multi-EGS groups Klopsch, Benjamin Thillaisundaram, Anitha Group Theory We study the distribution of normal subgroups in non-torsion, regular branch multi-EGS groups and show that the congruence completions of such groups have bounded finite central width. In particular, we show that the profinite completion of the Fabrykowski--Gupta group acting on the $p$-adic tree has central width 2 for every odd prime $p$. The methods used also apply to the family of Sunic groups, which closely resemble the Grigorchuk group. |
| title | Normal subgroups of non-torsion multi-EGS groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2509.08576 |