# 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 propertiesVIEW 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