Composition factor-unique group: Difference between revisions

Latest revision as of 00:22, 15 November 2008

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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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

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.

Revision as of 00:21, 15 November 2008 (view source) Vipul (talk \| contribs) (→‎Relation with other properties) ← Older edit		Latest revision as of 00:22, 15 November 2008 (view source) Vipul (talk \| contribs) (→‎Relation with other properties)
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	===Weaker properties===		===Weaker properties===

	* [[Stronger than::Group of finite composition length]]: ~~{{proofofstrictimplicationat\|\|~~[[~~Finite composition length~~ not implies composition factor-unique]]}}		* [[Stronger than::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]].