A subgroup property p is said to be simple-complete if it satisfies ... * p is trim, viz in every group, the trivial subgroup and the whole ... ...
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operator from the collection of trim subgroup properties to the group property ... (A subgroup property is trim if it is satisfied by both the whole ... ...
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The property of being a serial subgroup is obtained by applying the ... * Weaker than::Ascendant subgroup
* Weaker than::Descendant subgroup ... ...
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A subgroup H of a group G is termed cyclonormal if for any g \in G ... * Malnormal subgroup
* cyclic subgroup
==Metaproperties== ... ...
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A subgroup H of a group G is termed paracharacteristic in G if for ... * Weaker than::Intermediately isomorph-conjugate subgroup ... ...
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A subgroup H of a group G is termed polycharacteristic in G if the ... * Weaker than::Characteristic subgroup
* Weaker than::Procharacteristic ... ...
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A subgroup of a group is termed right-transitively conjugate-permutable ... * Weaker than::SCAB-subgroup
* Weaker than::Base of a wreath product ... ...
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A subgroup H of a group G is termed strongly permutably complemented ... * Stronger than::Permutably complemented subgroup
* Stronger than::Lattice ... ...
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A subgroup of a group is termed centrally closed or a CC-subgroup ... A subgroup H of a group G is termed centrally closed or a CC-subgroup ... ...
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A subgroup of a group is termed a join of finitely many 2-subnormal ... * Weaker than::2-subnormal subgroup
* Weaker than::Normal subgroup ... ...
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A subgroup H of a group G is termed a sub-homomorph-containing subgroup ... defining ingredient::homomorph-containing subgroup of H_{i+1}. ... ...
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A subgroup of a group is termed an intersection-transitively central ... | Weaker than::Central subgroup || contained in the center || any ... ...
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A subgroup H of a group G is termed image-closed fully invariant in ... * Weaker than::Verbal subgroup
* Weaker than::Normal Sylow subgroup ... ...
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A subgroup of a group is termed a characteristic transitively normal ... # It is both a characteristic subgroup and a transitively normal subgroup. ... ...
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A subgroup H of a group G is termed transfer-closed fully invariant ... transfer condition operator|fully invariant subgroup
==Relation with ... ...
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A subgroup of a group is termed a conjugacy-closed characteristic ... * Stronger than::Conjugacy-closed normal subgroup
* Stronger than::Transitively ... ...
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A subgroup of a group is termed an IA-automorphism-balanced subgroup ... * Weaker than::Perfect IA-automorphism-invariant subgroup ... ...
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A subgroup of a group is termed an AEP-subgroup or Automorphism Extension ... A subgroup H of a group G is termed an AEP subgroup of G if given ... ...
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simple if it has no proper nontrivial ascendant subgroup. ... applying the simple group operator to the trim subgroup property of being ... ...
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A subgroup of a group is termed a CEP subgroup (or a group with Congruence ... A subgroup H of a group G is termed a CEP subgroup if for any normal ... ...
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