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Proceedings of the American Mathematical Society

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On the conjugacy of injectors

Author: Graham A. Chambers
Journal: Proc. Amer. Math. Soc. 28 (1971), 358-360
MSC: Primary 20.40
MathSciNet review: 0277612
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Abstract: In their paper, Injektoren endlicher auflösbarer Gruppen, Fischer, Gaschütz and Hartley ask the following question. If $ \mathfrak{F}$ is a normal subgroup closed class of groups and if $ G$ is a finite solvable group which possesses $ \mathfrak{F}$-injectors, is it true that any two $ \mathfrak{F}$-injectors of $ G$ are conjugate in $ G$? A partial answer is given. It is proven that if $ G$ has $ p$-length 1 for each prime $ p$, then the answer to this question is yes.

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

  • [1] G. A. Chambers, $ p$-normally embedded subgroups of finite soluble groups, J. Algebra 16 (1970), 442-455. MR 0268275 (42:3174)
  • [2] B. Fischer, W. Gaschütz and B. Hartley, Injektoren endlicher auflösbarer Gruppen, Math. Z. 102 (1967), 337-339. MR 36 #6504. MR 0223456 (36:6504)
  • [3] B. Hartley, On Fischer's dualization of formation theory, Proc. London Math. Soc. (3) 19 (1969), 193-207. MR 39 #5696. MR 0244381 (39:5696)

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Keywords: Finite solvable group, Fitting class, injector, $ p$-normally embedded subgroup
Article copyright: © Copyright 1971 American Mathematical Society

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