FiniteGroups / CONCEPT
Minimal normal factors and the socle
Actual minimal normal subgroups form a characteristic socle. When that socle fills a centerless group, its factors are nonabelian simple and fully independent.
Closed
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES1
PROOF DEPTH0
DOCUMENT LINKS1
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
None recorded in this release.
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Actual minimal-normal factor orbitsstructural-affinity · Closed
- Ambient conjugacy of the actual factorsstructural-affinity · Closed
- Elementary minimal normal structurestructural-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 subgroups and smaller quotientsstructural-affinity · Closed
- Simple sections of finite productsstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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