On relative $\mathfrak {F}$-normalizers in finite solvable groups
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- by Patrick DβArcy
- Proc. Amer. Math. Soc. 42 (1974), 381-384
- DOI: https://doi.org/10.1090/S0002-9939-1974-0332956-4
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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. Hallβs 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), 175β202. MR 206089, DOI 10.1016/0021-8693(67)90034-8
- Patrick DβArcy, ${\mathfrak {F}}$-abnormality and the theory of finite solvable groups, J. Algebra 28 (1974), 342β361. MR 367051, DOI 10.1016/0021-8693(74)90045-3
- C. J. Graddon, ${\mathfrak {F}}$-reducers in finite soluble groups, J. Algebra 18 (1971), 574β587. 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), 51β61. MR 292937, DOI 10.1112/jlms/s2-4.1.51 P. Hall, On the system normalizers of a soluble group, Proc. London Math. Soc. 43 (1937), 507-528.
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 381-384
- MSC: Primary 20D10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0332956-4
- MathSciNet review: 0332956