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Abelian Frattini subgroup implies centralizer is critical
Abelian characteristic is not join-closed
Additive group of a field implies characteristic in holomorph
Additive group of a field implies monolith in holomorph
Center not is image-closed characteristic
Center not is intermediately characteristic
Centralizer of derived subgroup has class at most two
Characteristic and self-centralizing implies coprime automorphism-faithful
Characteristic central factor of WNSCDIN implies WNSCDIN
Characteristic direct factor not implies fully invariant
Characteristic upper-hook AEP implies characteristic
Characteristically complemented characteristic is transitive
Characteristically metacyclic group
Characteristically metacyclic not implies metacyclic derived series
Characteristically simple and non-abelian implies automorphism group is complete
Characteristically simple and non-abelian implies monolith in automorphism group
Characteristically simple and normal fully normalized implies minimal normal
Characteristically simple implies CSCFN-realizable
Cofactorial automorphism-invariant implies left-transitively 2-subnormal
Complemented characteristic not implies left-transitively complemented normal
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