On the conjugacy of injectors
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- by Graham A. Chambers PDF
- Proc. Amer. Math. Soc. 28 (1971), 358-360 Request permission
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
- Graham A. Chambers, $p$-normally embedded subgroups of finite soluble groups, J. Algebra 16 (1970), 442–455. MR 268275, DOI 10.1016/0021-8693(70)90018-9
- B. Fischer, W. Gaschütz, and B. Hartley, Injektoren endlicher auflösbarer Gruppen, Math. Z. 102 (1967), 337–339 (German). MR 223456, DOI 10.1007/BF01111070
- B. Hartley, On Fischer’s dualization of formation theory, Proc. London Math. Soc. (3) 19 (1969), 193–207. MR 244381, DOI 10.1112/plms/s3-19.2.193
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 358-360
- MSC: Primary 20.40
- DOI: https://doi.org/10.1090/S0002-9939-1971-0277612-3
- MathSciNet review: 0277612