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arXiv · 2509.08576

Normal subgroups of non-torsion multi-EGS groups

Benjamin Klopsch·Anitha Thillaisundaram
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Abstract

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.

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Benjamin Klopsch, Anitha Thillaisundaram. 2025-09-10. Normal subgroups of non-torsion multi-EGS groups. https://arxiv.org/abs/2509.08576

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