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A (finite) quasinilpotent group $G$ is one that satisfies $\mathrm{F}^{\ast}(G)=G$, where $\mathrm{F}^{\ast}$ is the generalised Fitting subgroup of $G$. The class of quasinilpotent groups is a formation (cf. Huppert & Blackburn Finite Groups III p.124), thus every (finite) group has a quasinilpotent residual, i.e. a smallest normal subgroup such that the quotient it affords is quasinilpotent.

My question is: how might one go about constructing the quasinilpotent residual with GAP?

the_fox
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  • There is a package FORMAT (http://www.gap-system.org/Packages/format.html) to work with formations. – ahulpke Nov 29 '16 at 23:01
  • I know about that particular package, but I don't quite see how to define the formation of quasinilpotent groups within it. – the_fox Dec 04 '16 at 09:22

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