On dicyclic groups as inner mapping groups of finite loops
Emma Leppälä, Markku Niemenmaa (2016)
Commentationes Mathematicae Universitatis Carolinae
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Let be a finite group with a dicyclic subgroup . We show that if there exist -connected transversals in , then is a solvable group. We apply this result to loop theory and show that if the inner mapping group of a finite loop is dicyclic, then is a solvable loop. We also discuss a more general solvability criterion in the case where is a certain type of a direct product.