ProCGroups.CompletedGroupAlgebra.Basic.InClass

6 sections | 6 files | 48 declarations

This is the public aggregate for the completion indexed by a finite-group class \(C\). It exports the in-class quotient indices and stages, their inverse system, the opaque named carrier, its coefficient algebra, canonical bundled projections, and the inherited inverse-limit topology.

The API deliberately mirrors the all-finite aggregate: use completedGroupAlgebraProjectionInClass, completedGroupAlgebraInClass_ext, and completedGroupAlgebraInClassCompatibleFamilyEquiv instead of constructing or projecting the compatible-family subtype directly.

import
Imported by

Index

1 file | 5 declarations | 2 Theorems | 1 Definition | 2 Abbreviations
This module defines the reverse-ordered open normal subgroups whose quotients lie in a finite-group class \(C\), together with their finite quotient groups and canonical quotien...

LimitAlgebra

1 file | 12 declarations | 2 Theorems | 5 Definitions | 5 Instances
This module gives the \(C\)-indexed completion the same opaque-carrier API as the all-finite completion. Its inverse-limit representation is exchanged explicitly, while projecti...

Projection

1 file | 7 declarations | 4 Theorems | 3 Definitions
This module bundles the canonical \(C\)-indexed finite-stage projection as ring, algebra, linear, and continuous linear maps. The underlying projection and compatibility theorem...

Stage

1 file | 14 declarations | 11 Theorems | 2 Definitions | 1 Abbreviation
This module defines the \(C\)-indexed finite group-algebra stages, their transition and coefficient-change ring homomorphisms, and the compatibility identities used by the inver...

System

1 file | 2 declarations | 1 Definition | 1 Instance
This module assembles the \(C\)-indexed stages into a topological inverse system and supplies the single `IsRingSystem` witness from which the completed carrier inherits its rin...

Topology

1 file | 8 declarations | 5 Theorems | 3 Instances
This module transports finite-stage topological structures through the named \(C\)-indexed inverse-limit carrier and records its compactness and separation properties.