Implications of the index of a fixed point subgroup
Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 1-7.
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Let G be a finite group and AAut(G). The index |G:C G (A)| 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 AAut(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.

Publié le :
DOI : 10.4171/RSMUP/26
Classification : 20, 00
Mots clés : Index, fixed point subgroup, automorphism of a group, solvable group, fitting height
Türkan, Erkan Murat 1

1 Çankaya University, Ankara, Turkey and Middle East Technical University, Ankara, Turkey
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     title = {Implications of the index of a fixed point subgroup},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {1--7},
     publisher = {European Mathematical Society Publishing House},
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     volume = {142},
     year = {2019},
     doi = {10.4171/RSMUP/26},
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Türkan, Erkan Murat. Implications of the index of a fixed point subgroup. Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 1-7. doi : 10.4171/RSMUP/26. http://www.numdam.org/articles/10.4171/RSMUP/26/

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