Frobenius action on Carter subgroups

Date

2020-08-01

Author

Ercan, Gülin

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Let G he a finite solvable group and H be a subgroup of Aut(G). Suppose that there exists an H-invariant Carter subgroup F of G such that the semidirect product FH is a Frobenius group with kernel F and complement H. We prove that the terms of the Fitting series of C-G (H) are obtained as the intersection of C-G (H) with the corresponding terms of the Fitting series of G, and the Fitting height of G may exceed the Fitting height of C-G (H) by at most one. As a corollary it is shown that for any set of primes pi, the terms of the pi-series of C-G (H) are obtained as the intersection of C-G (H) with the corresponding terms of the pi-series of G, and the pi-length of C may exceed the pi-length of C-G (H) by at most one. These theorems generalize the main results in [E. I. Khukhro, Fitting height of a finite group with a Frobenius group of automorphisms, J. Algebra 366 (2012) 1-11] obtained by Khukhro.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/56495

Journal

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION

DOI

https://doi.org/10.1142/s0218196720500319

Collections

Department of Mathematics, Article

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Citation Formats

G. Ercan, “Frobenius action on Carter subgroups,” INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, pp. 1073–1080, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56495.