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This is a Quantitative Study study.

October 17, 2025Open Access

Cohomology of solvable saturable pro-p groups and Lie algebras

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The n-th mod-p cohomology of solvable saturable pro-p groups is isomorphic to its associated Lie algebra.
Cohomology groups maintain isomorphic relationships when passing from Lie algebra g to g/p g.
Results establish a foundational link between group theory and algebraic structures for odd primes.
Implications extend to understanding cohomological dimensions in algebraic topology and number theory.

Implication

This analysis shows isomorphism between mod-p cohomology of solvable pro-p groups and their Lie algebras as F_p-vector spaces.

Abstract

Let p be an odd prime, and let n∈ be an integer. We show that the nᵗʰ mod-p cohomology of a solvable saturable pro-p group is isomorphic to the nᵗʰ mod-p cohomology of its associated ₚ-Lie algebra as a ₚ-vector space. Addittonally, we obtain that the nᵗʰ mod-p cohomology of and of /p are isomorphic as ₚ-vector spaces.

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Cite This Study

Ocaña et al. (2025) studied this question.

synapsesocial.com/papers/68f19f20de32064e504ddf4c https://doi.org/10.48550/arxiv.2507.18163

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Implication

This analysis shows isomorphism between mod-p cohomology of solvable pro-p groups and their Lie algebras as F_p-vector spaces.

Cohomology of solvable saturable pro-p groups and Lie algebras

Key Points

Implication

Abstract

Discussion

Cite This Study

Cohomology of solvable saturable pro-p groups and Lie algebras

Key Points

Implication

Abstract

Discussion

Cite This Study

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