On central nilpotency in finite loops with nilpotent inner mapping groups

Niemenmaa, Markku, and Rytty, Miikka. "On central nilpotency in finite loops with nilpotent inner mapping groups." Commentationes Mathematicae Universitatis Carolinae 49.2 (2008): 271-277. <http://eudml.org/doc/250450>.

@article{Niemenmaa2008,
abstract = {In this paper we consider finite loops whose inner mapping groups are nilpotent. We first consider the case where the inner mapping group $I(Q)$ of a loop $Q$ is the direct product of a dihedral group of order $8$ and an abelian group. Our second result deals with the case where $Q$ is a $2$-loop and $I(Q)$ is a nilpotent group whose nonabelian Sylow subgroups satisfy a special condition. In both cases it turns out that $Q$ is centrally nilpotent.},
author = {Niemenmaa, Markku, Rytty, Miikka},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; group; connected transversals; finite loops; nilpotent inner mapping groups; connected transversals},
language = {eng},
number = {2},
pages = {271-277},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On central nilpotency in finite loops with nilpotent inner mapping groups},
url = {http://eudml.org/doc/250450},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Niemenmaa, Markku
AU - Rytty, Miikka
TI - On central nilpotency in finite loops with nilpotent inner mapping groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 2
SP - 271
EP - 277
AB - In this paper we consider finite loops whose inner mapping groups are nilpotent. We first consider the case where the inner mapping group $I(Q)$ of a loop $Q$ is the direct product of a dihedral group of order $8$ and an abelian group. Our second result deals with the case where $Q$ is a $2$-loop and $I(Q)$ is a nilpotent group whose nonabelian Sylow subgroups satisfy a special condition. In both cases it turns out that $Q$ is centrally nilpotent.
LA - eng
KW - loop; group; connected transversals; finite loops; nilpotent inner mapping groups; connected transversals
UR - http://eudml.org/doc/250450
ER -