Implications of the index of a fixed point subgroup


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Turkan E. M.

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, cilt.142, ss.1-7, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 142
  • Basım Tarihi: 2019
  • Doi Numarası: 10.4171/rsmup/26
  • Dergi Adı: RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA
  • Sayfa Sayıları: ss.1-7

Özet

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.