On dicyclic groups as inner mapping groups of finite loops

Leppälä, Emma, and Niemenmaa, Markku. "On dicyclic groups as inner mapping groups of finite loops." Commentationes Mathematicae Universitatis Carolinae 57.4 (2016): 549-553. <http://eudml.org/doc/287562>.

@article{Leppälä2016,
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.},
author = {Leppälä, Emma, Niemenmaa, Markku},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {solvable loop; inner mapping group; dicyclic group},
language = {eng},
number = {4},
pages = {549-553},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On dicyclic groups as inner mapping groups of finite loops},
url = {http://eudml.org/doc/287562},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Leppälä, Emma
AU - Niemenmaa, Markku
TI - On dicyclic groups as inner mapping groups of finite loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 4
SP - 549
EP - 553
AB - 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.
LA - eng
KW - solvable loop; inner mapping group; dicyclic group
UR - http://eudml.org/doc/287562
ER -