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Proceedings of the American Mathematical Society

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On relative $ \mathfrak{F}$-normalizers in finite solvable groups

Author: Patrick D’Arcy
Journal: Proc. Amer. Math. Soc. 42 (1974), 381-384
MSC: Primary 20D10
MathSciNet review: 0332956
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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. Hall's relative system normalizers to an arbitrary subgroup of a given finite solvable group.

References [Enhancements On Off] (What's this?)

  • [1] Roger Carter and Trevor Hawkes, The \cal𝐹-normalizers of a finite soluble group, J. Algebra 5 (1967), 175–202. MR 0206089
  • [2] Patrick D’Arcy, 𝔉-abnormality and the theory of finite solvable groups, J. Algebra 28 (1974), 342–361. MR 0367051
  • [3] C. J. Graddon, 𝔉-reducers in finite soluble groups, J. Algebra 18 (1971), 574–587. MR 0280591
  • [4] C. J. Graddon, The relation between 𝔉-reducers and 𝔉-subnormalizers in finite soluble groups, J. London Math. Soc. (2) 4 (1971), 51–61. MR 0292937
  • [5] P. Hall, On the system normalizers of a soluble group, Proc. London Math. Soc. 43 (1937), 507-528.
  • [6] B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703

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Keywords: Finite solvable group, locally defined formation, $ \mathfrak{F}$-reducer, relative $ \mathfrak{F}$-normalizer
Article copyright: © Copyright 1974 American Mathematical Society