On the structure of finite loop capable nilpotent groups
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 349-355
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In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either $C_{p^k} \times C_{p^l}$, $k > l \geq 0$ as the Sylow $p$-subgroup for some odd prime $p$ or the group of quaternions as the Sylow $2$-subgroup may not be loop capable.
In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either $C_{p^k} \times C_{p^l}$, $k > l \geq 0$ as the Sylow $p$-subgroup for some odd prime $p$ or the group of quaternions as the Sylow $2$-subgroup may not be loop capable.
@article{CMUC_2010_51_2_a17,
author = {Rytty, Miikka},
title = {On the structure of finite loop capable nilpotent groups},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {349--355},
year = {2010},
volume = {51},
number = {2},
mrnumber = {2682486},
zbl = {1211.20021},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2010_51_2_a17/}
}
Rytty, Miikka. On the structure of finite loop capable nilpotent groups. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 349-355. http://geodesic.mathdoc.fr/item/CMUC_2010_51_2_a17/