Almost solvable group

This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)
View other properties of finite groups OR View all group properties

You might be looking for: virtually solvable group

Definition

Symbol-free definition

A finite group is termed almost solvable if it satisfies the following equivalent conditions:

• The quotient by its solvable radical is either trivial, or isomorphic to the alternating group on five letters
• The group is a $M_{4}$-group: every irreducible character is induced from a character on a subgroup of dimension at most $4$

Relation with other properties

Stronger properties

• Finite solvable group