An Application of Finite Groups to Hopf algebras
Keywords:Hopf algebras, Integral elements, Semisimple Hopf algebra, Left coideal subalgebra, Solvability of groups and Hopf algebras, Nilpotency of groups and Hopf algebras.
Kaplanskyâ€™s famous conjectures about generalizing results from groups to Hopf al-
gebras inspired many mathematicians to try to find solusions for them. Recently, Cohen and Westreich in  and  have generalized the concepts of nilpotency and solvability of groups to Hopf algebras under certain conditions and proved interesting results. In this article, we follow their work and give a detailed example by considering a finite group G and an algebraically closed field K. In more details, we construct the group Hopf algebra H = KG and examine its properties to see what of the properties of the original finite group can be carried out in the case of H.
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