Turkan, Erkan Murat2020-02-282025-09-182020-02-282025-09-182019Turkan, Erkan Murat, "Implications of the index of a fixed point subgroup", Rendiconti Del Seminario Matematico Della Universita Di Padova", Rendiconti Del Seminario Matematico Della Universita Di Padova, Vol. 142, pp. 1-7, (2019).0041-89942240-2926https://doi.org/10.4171/RSMUP/26https://hdl.handle.net/20.500.12416/10756Let 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.eninfo:eu-repo/semantics/closedAccessIndexFixed Point SubgroupAutomorphism Of A GroupSolvable GroupFitting HeightArticle10.4171/RSMUP/262-s2.0-85090253708