Geodesic
On Semisimple Hopf Algebras of Dimension pq n
Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 264-269

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Let $p$ , $q$ be prime numbers with ${{p}^{2}}\,<\,q,\,n\,\in \,\mathbb{N}$ , and $H$ a semisimple Hopf algebra of dimension $p{{q}^{n}}$ over an algebraically closed field of characteristic 0. This paper proves that $H$ must possess one of the following two structures: (1) $H$ is semisolvable; (2) $H$ is a Radford biproduct $R\#kG$ , where $kG$ is the group algebra of group $G$ of order $p$ and $R$ is a semisimple Yetter–Drinfeld Hopf algebra in $_{kG}^{kG}y\mathcal{D}$ of dimension ${{q}^{n}}$ .
DOI : 10.4153/CMB-2014-003-0
Mots-clés : 16W30, semisimple Hopf algebra, semisolvability, Radford biproduct, Drinfeld double 
Dai, Li; Dong, Jingcheng. On Semisimple Hopf Algebras of Dimension pq n. Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 264-269. doi: 10.4153/CMB-2014-003-0
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     title = {On {Semisimple} {Hopf} {Algebras} of {Dimension} pq n},
     journal = {Canadian mathematical bulletin},
     pages = {264--269},
     year = {2014},
     volume = {57},
     number = {2},
     doi = {10.4153/CMB-2014-003-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-003-0/}
}
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