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October 8, 2025Open Access

Powerful subgroups of extensions of powerful p-groups and pro-p groups

Key Points

The result shows that lower series terms are powerfully embedded in pro-p groups under specific conditions.
It is established that if the quotient group is a powerful group, the structure of the pro-p group is preserved.
The findings are extended to non-finitely generated pro-p groups, contingent on additional criteria.
Conditions imposed expand the understanding of p-adic analytic characteristics in these groups.

Abstract

Let H be a finitely generated pro- p group. We prove that, if H/Z₍-₁ (H) is a powerful group, then the n-th terms of the lower p-series and the lower central series of H are powerfully embedded in H. As a consequence, we obtain that if H/Zₙ (H) is a p-adic analytic pro-p group for some positive integer n, then H is a p -adic analytic pro- p group. Furthermore, we extend these results to pro- p groups that are not necessarily finitely generated, provided some additional conditions are imposed.

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Cite This Study

Kalithasan et al. (Wed,) studied this question.

synapsesocial.com/papers/68e62de1a8c0c6d458740094 https://doi.org/https://doi.org/10.48550/arxiv.2503.15240

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