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H. Heineken, W. Herfort, Gil Kaplan:
"Nilpotency, Solvability and the Twisting Function of Finite Groups II";
Archiv der Mathematik (invited), Volume 102 (2014), 6; 12 pages.

Let G be a finite group and m a natural number. The twisting function with m variables
on G is defined by \tau_m(x_1,\cdots,x_m):=(x_1^{x_2},...,x_{m-1}^{x_m},x_m^{x_1}) and has
been introduced and studied by the third author. In the current paper we extend and
sharpen known results on solvability and nilpotency. Furthermore, for groups G such that \tau_2 is a permutation on the
cartesian product GxG, we investigate the order of this permutation and its connection to
properties of G.

Die "Twistingfunktion" wurde von Gil Kaplan in einer früheren Arbeit definiert. Sie ist für nilpotente Gruppen stets eine Bijektion und ihre Kenntnis ermöglicht Aussagen über eine vorgegebene Gruppe. Entsprechende Aussagen werden in dieser Arbeit gemacht.

Nilpotency, Solvability, Sylow subgroups, Fitting subgroup, 2-transitive permutation groups

http://dx.doi.org/10.1007/s00013-014-0656-y