The aim of this article is to study the influence of a finite group of prime power order on the structure of specific types of algebras. In more details, we consider a finite group  of prime power order and construct a bicrossproduct Hopf algebra associated with a factorization of this finite group X. Furthermore, we discuss which property of X can be carried out to the induced bicrossproduct Hopf algebra

solvable groups, nilpotent groups, bicrossproduct Hopf algebras, solvability of Hopf algebras, nilpotency of Hopf algebras.

Received: May 12, 2021; Accepted: June 7, 2021; Published: July 3, 2021

How to cite this article: Bashayer M. Alyoubi and M. M. Al-Shomrani, The groups of prime power order and the structure of hopf algebras, JP Journal of Algebra, Number Theory and Applications 51(2) (2021), 145-182. DOI: 10.17654/NT051020145

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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