Bounded-solvable IAPS

This term is related to: APS theory
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This article defines a property that can be evaluated for an IAPS of groups

ANALOGY: This is an analogue in IAPS of a property encountered in group. Specifically, it is a IAPS property analogous to the group property: solvable group
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Definition

An IAPS of groups is termed a bounded-solvable IAPS if it satisfies the following equivalent conditions:

• Every member is a solvable group, and there is a common finite bound on the solvable lengths of all the members
• The derived sub-IAPS series terminates, in finitely many steps, at the identity.

Relation with other properties

Stronger properties

• Abelian IAPS
• Bounded-nilpotent IAPS

Weaker properties

• Solvable IAPS