Composition factor-unique group

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Definition

Symbol-free definition

A group is said to be composition factor-unique if the order in which its composition factors occur is the same for every composition series.

Relation with other properties

Stronger properties

• Characteristically simple group
• Group of prime power order
• Composition series-unique group

Weaker properties

• Group of finite composition length: For a proof that the order of composition factors need not be the same for all composition series, refer finite not implies composition factor-unique.