On relative 𝔉-normalizers in finite solvable groups

D’Arcy, Patrick

doi:10.1090/S0002-9939-1974-0332956-4

On relative $\mathfrak {F}$-normalizers in finite solvable groups
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Proc. Amer. Math. Soc. 42 (1974), 381-384 Request permission

Abstract:

In the theory of saturated formations of finite solvable groups, certain subgroups, called $\mathfrak {F}$-reducers, have been considered. In this note it is pointed out that the work of an $\mathfrak {F}$-reducer R is done by certain subsets of R, subsets that can be considered generalizations of P. Hall’s relative system normalizers to an arbitrary subgroup of a given finite solvable group.

References

Roger Carter and Trevor Hawkes, The ${\cal F}$-normalizers of a finite soluble group, J. Algebra 5 (1967), 175–202. MR 206089, DOI 10.1016/0021-8693(67)90034-8
Patrick D’Arcy, ${\mathfrak {F}}$-abnormality and the theory of finite solvable groups, J. Algebra 28 (1974), 342–361. MR 367051, DOI 10.1016/0021-8693(74)90045-3
C. J. Graddon, ${\mathfrak {F}}$-reducers in finite soluble groups, J. Algebra 18 (1971), 574–587. MR 280591, DOI 10.1016/0021-8693(71)90140-2
C. J. Graddon, The relation between ${\mathfrak {F}}$-reducers and ${\mathfrak {F}}$-subnormalizers in finite soluble groups, J. London Math. Soc. (2) 4 (1971), 51–61. MR 292937, DOI 10.1112/jlms/s2-4.1.51

On the system normalizers of a soluble group

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B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703