Group of finite composition length
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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of finiteness (groups)|Find other variations of finiteness (groups) |
This property makes sense for infinite groups. For finite groups, it is always true
Definition
A group is said to have finite composition length if it satisfies the following equivalent conditions:
- It possesses a composition series of finite length, viz., a subnormal series such that all the successive quotients are simple groups.
- It satisfies both the ascending chain condition on subnormal subgroups and the descending chain condition on subnormal subgroups.