FiniteGroups / CONCEPT
Elementary minimal normal structure
A nonabelian minimal nontrivial normal subgroup of a finite ambient group is perfect and centerless, and its canonical internal product of actual minimal normal factors is isomorphic to it.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES1
PROOF DEPTH2
DOCUMENT LINKS1
The elementary nonabelian decomposition
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Actual minimal-normal factor orbitsstructural-affinity · Closed
- Ambient conjugacy of the actual factorsstructural-affinity · Closed
- Bounded lifts of a fixed quotient tuplestructural-affinity · Closed
- From transitive blocks to conditional absorptionstructural-affinity · Closed
- Gaschutz Lifting with an Arbitrary Fixed Setstructural-affinity · Closed
- Generator decomposition under explicit absorptionstructural-affinity · Closed
- Large minimal normal subgroupsstructural-affinity · Closed
- Minimal normal factors and the soclestructural-affinity · Closed
- Minimal normal subgroups and smaller quotientsstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
Loading release versions...
Browse the archiveCertified provenance