Minimax group
From Groupprops
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
This property makes sense for infinite groups. For finite groups, it is always true
Contents
Definition
A group is said to be a minimax group if it has a subnormal series of finite length such that each successive quotient satisfies either the minimum condition on subgroups (i.e., is an Artinian group) or the maximum condition on subgroups (i.e., is a Noetherian group).
Relation with other properties
Stronger properties
Conjunction with other properties
- Solvable minimax group is the conjunction with the property of being a solvable group
