Implications of the index of a fixed point subgroup

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2019-01-01

Author

Turkan, Erkan Murat

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Let G be a finite group and A <= Aut(G). The index vertical bar G:C-G(A)vertical bar is called the index of A in G and is denoted by Ind(G)(A). In this paper, we study the influence of Ind(G)(A) on the structure of G and prove that [G, A] is solvable in case where A is cyclic, Ind G(A) is squarefree and the orders of G and A are coprime. Moreover, for arbitrary A <= Aut(G) whose order is coprime to the order of G, we show that when [G, A] is solvable, the Fitting height of [G, A] is bounded above by the number of primes (counted with multiplicities) dividing Ind(G)(A) and this bound is best possible.

Subject Keywords

Mathematical Physics, Geometry and Topology, Algebra and Number Theory, Analysis

URI

https://hdl.handle.net/11511/63724

Journal

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA

DOI

https://doi.org/10.4171/rsmup/26

Collections

Department of Mathematics, Article

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Citation Formats

E. M. Turkan, “Implications of the index of a fixed point subgroup,” RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, pp. 1–7, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63724.