Composition series-unique group

From Groupprops
(Redirected from Jordan-unique group)
Jump to: navigation, search
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions


BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

Definition

Symbol-free definition

A group is said to be composition series-unique if it has a unique composition series. In the case of a finite group, this can be expressed inductively as saying that that group is one-headed and that the head (viz the unique maximal normal subgroup) is itself composition series-unique.

Relation with other properties

Stronger properties

Weaker properties

Opposite properties