Groups of automorphisms with TNI-centralizers

Date

2018-03-15

Author

Ercan, Gülin

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A subgroup H of a finite group G is called a TNI-subgroup if N-G(H) boolean AND H-9 = 1 for any g is an element of G \ N-G (H). Let A be a group acting on G by automorphisms where C-G(A) is a TNI-subgroup of G. We prove that G is solvable if and only if C-G(A) is solvable, and determine some bounds for the nilpotent length of G in terms of the nilpotent length of C-G(A) under some additional assumptions. We also study the action of a Frobenius group FH of automorphisms on a group G if the set of fixed points C-G(F) of the kernel F forms a TNI-subgroup, and obtain a bound for the nilpotent length of G in terms of the nilpotent lengths of C-G(F) and C-G(H).

Subject Keywords

TNI-subgroup, Automorphism, Centralizer, Frobenius group

URI

https://hdl.handle.net/11511/39221

Journal

JOURNAL OF ALGEBRA

DOI

https://doi.org/10.1016/j.jalgebra.2017.10.021

Collections

Department of Mathematics, Article

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Citation Formats

G. Ercan, “Groups of automorphisms with TNI-centralizers,” JOURNAL OF ALGEBRA, pp. 38–46, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39221.