On abelian group actions with TNI-centralizers

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2019-07-03

Author

Ercan, Gülin

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A subgroup H of a group G is said to be a TNI-subgroup if for any Let A be an abelian group acting coprimely on the finite group G by automorphisms in such a way that for all is a solvable TNI-subgroup of G. We prove that G is a solvable group with Fitting length h(G) is at most . In particular whenever is nonnormal. Here, h(G) is the Fitting length of G and is the number of primes dividing A counted with multiplicities.

Subject Keywords

Automorphism, Centralizer, Fitting length, TNI-subgroup

URI

https://hdl.handle.net/11511/39720

Journal

COMMUNICATIONS IN ALGEBRA

DOI

https://doi.org/10.1080/00927872.2018.1549662

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Department of Mathematics, Article

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Citation Formats

G. Ercan, “On abelian group actions with TNI-centralizers,” COMMUNICATIONS IN ALGEBRA, pp. 3003–3006, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39720.