FiniteGroups / CONCEPT
Ambient conjugacy of the actual factors
Ambient conjugates of a nontrivial subgroup fill a minimal normal subgroup; ambient conjugation is transitive on its nonabelian simple factors.
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DIRECT PREREQUISITES1
DIRECT CONSEQUENCES1
PROOF DEPTH3
DOCUMENT LINKS1
Ambient conjugation is transitive on factors
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
- Elementary minimal normal structurestructural-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
- Hall interval selection on actual permutation cyclesstructural-affinity · Closed
- Large minimal normal subgroupsstructural-affinity · Closed
- Minimal normal factors and the soclestructural-affinity · Closed
- Minimal normal subgroups and smaller quotientsstructural-affinity · Closed
- Sections of Arbitrary Subgroupsstructural-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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