Marginal subgroup of finite type

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup of a group is termed a marginal subgroup of finite type if it can be described in the following equivalent ways:

  1. It is the marginal subgroup corresponding to a single word.
  2. It is the marginal subgroup corresponding to a finite collection of words.

Examples

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
marginal subgroup of finite index |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
purely definable subgroup Purely positively definable subgroup|FULL LIST, MORE INFO
elementarily characteristic subgroup Purely definable subgroup|FULL LIST, MORE INFO
marginal subgroup |FULL LIST, MORE INFO
strictly characteristic subgroup invariant under all surjective endomorphisms Marginal subgroup, Purely positively definable subgroup|FULL LIST, MORE INFO
characteristic subgroup invariant under all automorphisms Elementarily characteristic subgroup, Marginal subgroup, Purely definable subgroup, Purely positively definable subgroup|FULL LIST, MORE INFO
normal subgroup invariant under all inner automorphisms Purely definable subgroup, Purely positively definable subgroup|FULL LIST, MORE INFO