Geodesic
On dicyclic groups as inner mapping groups of finite loops
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 4, pp. 549-553.

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Let $G$ be a finite group with a dicyclic subgroup $H$. We show that if there exist $H$-connected transversals in $G$, then $G$ is a solvable group. We apply this result to loop theory and show that if the inner mapping group $I(Q)$ of a finite loop $Q$ is dicyclic, then $Q$ is a solvable loop. We also discuss a more general solvability criterion in the case where $I(Q)$ is a certain type of a direct product.
DOI : 10.14712/1213-7243.2015.180
Classification : 20D10, 20N05
Keywords: solvable loop; inner mapping group; dicyclic group 
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Leppälä, Emma; Niemenmaa, Markku. On dicyclic groups as inner mapping groups of finite loops. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 4, pp. 549-553. doi : 10.14712/1213-7243.2015.180. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.180/

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