The pre-Frattini residual

Bechtell, H.

doi:10.1090/S0002-9939-1976-0409633-6

The pre-Frattini residual
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Proc. Amer. Math. Soc. 55 (1976), 267-270 Request permission

Abstract:

The structure of a prefrattini subgroup in a finite solvable group is related to the structure of the prefrattini residual, that is, the residual for the formation of solvable $nC$-groups. In particular this structure can be identified with the system normalizers of a lower nilpotent series in the prefrattini residual. Moreover, the prefrattini subgroups form a complete conjugate class within this residual and also contain the system normalizers of the residual.

References

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On the system normalizers of a solvable group

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