# On central nilpotency in finite loops with nilpotent inner mapping groups

Markku Niemenmaa; Miikka Rytty

Commentationes Mathematicae Universitatis Carolinae (2008)

- Volume: 49, Issue: 2, page 271-277
- ISSN: 0010-2628

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topNiemenmaa, 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 -

## References

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