This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
View a complete list of subgroup-defining functions OR View a complete list of quotient-defining functions
The permutation kernel of , denoted , is the kernel of the action of on these factors induced by the action of on by conjugation. contains the socle over solvable radical .
The permutation kernel is part of the Babai-Beals filtration of .