Frobenius groups of automorphisms with almost fixed point free kernel

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2019-03-01

Author

Ercan, Gülin

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Let FH be a Frobenius group with kernel F and complement H, acting coprimely on the finite solvable group G by automorphisms. We prove that if C-G(H) is of Fitting length n then the index of the n-th Fitting subgroup F-n(G) in G is bounded in terms of vertical bar C-G(F)vertical bar and vertical bar F vertical bar. This generalizes a result of Khukhro and Makarenko [6] which handles the case n = 1.

Subject Keywords

Solvable group, Automorphism, Fitting length, Frobenius group

URI

https://hdl.handle.net/11511/37246

Journal

JOURNAL OF ALGEBRA

DOI

https://doi.org/10.1016/j.jalgebra.2018.12.004

Collections

Department of Mathematics, Article

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Beauville structures in p-groups Gül, Şükran; Ercan, Gülin; Fernández-Alcober, Gustavo Adolfo; Department of Mathematics (2016) Given a finite group G and two elements x, y in G, we denote by Sigma(x,y) the union of all conjugates of the cyclic subgroups generated by x, y and xy. Then G is called a Beauville group of unmixed type if the following conditions hold: (i) G is a 2-generator group. (ii) G has two generating sets {x1,y1} and {x2, y2} such that Sigma (x1, y1) intersection Sigma(x2, y2) is 1. In this case, {x1, y1} and {x2, y2} are said to form a Beauville structure for G. The main purpose of this thesis is to extend the kn...

Citation Formats

G. Ercan, “Frobenius groups of automorphisms with almost fixed point free kernel,” JOURNAL OF ALGEBRA, pp. 384–389, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37246.