## Emma Leppälä, Markku Niemenmaa

*On dicyclic groups as inner mapping groups of finite loops*

Comment.Math.Univ.Carolin. 57,4 (2016) 549-553.**Abstract:**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.

**Keywords:** solvable loop; inner mapping group; dicyclic group

**DOI:** DOI 10.14712/1213-7243.2015.180

**AMS Subject Classification:** 20N05 20D10

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