Minimax group

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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This property makes sense for infinite groups. For finite groups, it is always true

Definition

Symbol-free 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 a slender group) or the maximum condition on subgroups (i.e., is a Artinian group).

Definition with symbols

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Relation with other properties

Stronger properties

• Finite group
• Slender group
• Artinian group

Conjunction with other properties

• Solvable minimax group is the conjunction with the property of being a solvable group