DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05

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Teichmuller lift in a splitting p-modular system

Definition

Fix a splitting $p$ -modular system $(K, O, k)$ for a finite group $G$ . If $λ \in k^{\times}$ has finite order prime to $p$ , its Teichmuller lift is the unique element $τ (λ) \in O^{\times}$ such that

$τ (λ)$ has the same finite order as $λ$ , hence order prime to $p$ , and
the image of $τ (λ)$ in $k^{\times}$ is $λ$ .

Thus $τ$ picks the prime-to- $p$ root of unity in $O^{\times}$ reducing to $λ$ .

Depends on

A splitting p-modular system for a finite group is a p-modular system whose fraction and residue fields split the needed group algebras

Used by

Brauer character of a finite-dimensional kG-module Definition
The Teichmuller lift is multiplicative and unique Lemma

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

J. Miquel Martinez, Modular Representation Theory of Finite Groups (standard reference, not scraped)
Tudor Ciurca, Representation Theory (standard reference, not scraped)