Groupprops, The Group Properties Wiki (pre-alpha)
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Hereditarily ACIC-group
From Groupprops
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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a group property: a property that can be evaluated to true/false for any given group
View a complete list of group properties
VIEW RELATED:
RANDOM GROUP PROPERTY: Complete group: A group for which the natural homomorphism to its automorphism group is an isomorphism, i.e., a centerless group for which every automorphism is inner.
Definition
A group is termed a hereditarily ACIC-group if every subgroup of it is an ACIC-group.
Formalisms
BEWARE! This section of the article uses terminology local to the wiki, possibly without giving a full explanation of the terminology used (though efforts have been made to clarify terminology as much as possible within the particular context)
In terms of the Hamiltonian operator
This property is obtained by applying the Hamiltonian operator to the property: ACIC-group
View other properties obtained by applying the Hamiltonian operator
Relation with other properties
Stronger properties
Weaker properties
Metaproperties
Subgroups
This group property is subgroup-closed, viz., any subgroup of a group satisfying the property also satisfies the property
View a complete list of subgroup-closed group properties
