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 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.
Publié le :
DOI : 10.4171/RSMUP/26
DOI : 10.4171/RSMUP/26
Classification :
20, 00
Mots-clés : Index, fixed point subgroup, automorphism of a group, solvable group, fitting height
Mots-clés : Index, fixed point subgroup, automorphism of a group, solvable group, fitting height
Affiliations des auteurs :
Türkan, Erkan Murat 1
@article{RSMUP_2019__142__1_0, author = {T\"urkan, Erkan Murat}, 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}, address = {Zuerich, Switzerland}, volume = {142}, year = {2019}, doi = {10.4171/RSMUP/26}, mrnumber = {4032800}, zbl = {1468.20054}, url = {http://www.numdam.org/articles/10.4171/RSMUP/26/} }
TY - JOUR AU - Türkan, Erkan Murat TI - Implications of the index of a fixed point subgroup JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2019 SP - 1 EP - 7 VL - 142 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/26/ DO - 10.4171/RSMUP/26 ID - RSMUP_2019__142__1_0 ER -
%0 Journal Article %A Türkan, Erkan Murat %T Implications of the index of a fixed point subgroup %J Rendiconti del Seminario Matematico della Università di Padova %D 2019 %P 1-7 %V 142 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/26/ %R 10.4171/RSMUP/26 %F RSMUP_2019__142__1_0
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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