Simple-complete subgroup property

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This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
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VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

Definition

Symbol-free definition

A subgroup property p is said to be simple-complete if it satisfies the following:

  • p is trim, viz in every group, the trivial subgroup and the whole group satisfy property p
  • Every group can be embedded in a group that is p-simple (that is, that satisfies the group property obtained by applying the simple group operator to p). In other words, every group can be embedded into a group that has no proper nontrivial subgroup satisfying p

Relation with other properties

Related properties