DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-04

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

Definition

Let $G$ be a finite group. A splitting $p$ -modular system for $G$ is a $p$ -modular system $(K, O, k)$ such that both $K$ and $k$ are splitting fields for every subgroup $H \leq G$ .

Thus the characteristic- $0$ fraction field and the characteristic- $p$ residue field satisfy the splitting-field condition of A splitting field for a finite group: every irreducible representation has scalar endomorphism ring simultaneously for the determinate family of subgroups of $G$ .

Depends on

Used by

An OG-lattice is a finite free module over the valuation ring with G-action, and reduction modulo the maximal ideal produces a kG-module Definition

Dependency tree · two levels

7 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

Peter Webb, A Course in Finite Group Representation Theory (23 Feb 2016 draft) (standard reference, not scraped)