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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0277612-3
PII: S 0002-9939(1971)0277612-3
Keywords: Finite solvable group, Fitting class, injector, $ p$-normally embedded subgroup
Article copyright: © Copyright 1971 American Mathematical Society