Composition series-unique group

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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

• Simple group
• Cyclic group of prime power order

Weaker properties

• Composition factor-unique group
• Group of finite composition length

Opposite properties

• Composition factor-permutable group