Marginal subgroup of finite type

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]

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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

• The center, and all members of the upper central series, are 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				|FULL LIST, MORE INFO
elementarily characteristic subgroup				|FULL LIST, MORE INFO
marginal subgroup				|FULL LIST, MORE INFO
strictly characteristic subgroup	invariant under all surjective endomorphisms			|FULL LIST, MORE INFO
characteristic subgroup	invariant under all automorphisms			|FULL LIST, MORE INFO
normal subgroup	invariant under all inner automorphisms			|FULL LIST, MORE INFO