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Groups of automorphisms with TNI-centralizers
Date
2018-03-15
Author
Ercan, Gülin
Metadata
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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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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.