Babai-Beals filtration

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Definition

Let G be a finite group. The Babai-Beals filtration of G is the following ascending chain of subgroups of G:

1 \le \operatorname{Sol}(G) \le \operatorname{Soc}^*(G) \le \operatorname{PKer}(G) \le G

where:

Here is what we can say about the successive quotients:

References