Homological growth of nilpotent-by-abelian pro-p groups

Dessislava H. Kochloukova; Aline G. S. Pinto

doi:10.48550/arxiv.2510.00421

October 1, 2025Open Access

Homological growth of nilpotent-by-abelian pro-p groups

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Key Points

The torsion-free rank of H_i(M, Z_p) has a finite upper bound for i ≤ m.
This result holds for pro-p groups of finite index in a group G of type FP_{2cm}.
Nilpotent-by-abelian properties play a critical role in understanding group structure.
The analysis emphasizes the behavior of homological growth in such groups.

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Implication

We show a finite bound on torsion-free rank of H_i(M, Z_p) in pro-p groups, suggesting structural stability.

Abstract

We show that the torsion-free rank of Hᵢ(M, Zₚ) has finite upper bound for i ≤ m, where M runs through the pro-p subgroups of finite index in a pro-p group G that is (nilpotent of class c)-by-abelian such that $ G/N'$ is of type FP2cm.

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Kochloukova et al. (2025) studied this question.

synapsesocial.com/papers/68e24e6fd6d66a53c2473f34 https://doi.org/10.48550/arxiv.2510.00421

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Homological growth of nilpotent-by-abelian pro-p groups

Key Points

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Implication

Abstract

Discussion

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Homological growth of nilpotent-by-abelian pro-p groups

Key Points

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Implication

Abstract

Discussion

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