Implications of the index of a fixed point subgroup

  • Erkan Murat Türkan

    Çankaya University, Ankara, Turkey and Middle East Technical University, Ankara, Turkey
Implications of the index of a fixed point subgroup cover

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Abstract

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

Cite this article

Erkan Murat Türkan, Implications of the index of a fixed point subgroup. Rend. Sem. Mat. Univ. Padova 142 (2019), pp. 1–7

DOI 10.4171/RSMUP/26