Odd order semidirect extensions of commutative automorphic loops
Commentationes Mathematicae Universitatis Carolinae (2014)
- Volume: 55, Issue: 4, page 447-456
- ISSN: 0010-2628
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topJedlička, Přemysl. "Odd order semidirect extensions of commutative automorphic loops." Commentationes Mathematicae Universitatis Carolinae 55.4 (2014): 447-456. <http://eudml.org/doc/261987>.
@article{Jedlička2014,
abstract = {We analyze semidirect extensions of middle nuclei of commutative automorphic loops. We find a less complicated conditions for the semidirect construction when the middle nucleus is an odd order abelian group. We then use the description to study extensions of orders $3$ and $5$.},
author = {Jedlička, Přemysl},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {automorphic loop; semidirect product; middle nucleus; cyclic group; commutative automorphic loops; semidirect products; middle nucleus; cyclic groups},
language = {eng},
number = {4},
pages = {447-456},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Odd order semidirect extensions of commutative automorphic loops},
url = {http://eudml.org/doc/261987},
volume = {55},
year = {2014},
}
TY - JOUR
AU - Jedlička, Přemysl
TI - Odd order semidirect extensions of commutative automorphic loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 4
SP - 447
EP - 456
AB - We analyze semidirect extensions of middle nuclei of commutative automorphic loops. We find a less complicated conditions for the semidirect construction when the middle nucleus is an odd order abelian group. We then use the description to study extensions of orders $3$ and $5$.
LA - eng
KW - automorphic loop; semidirect product; middle nucleus; cyclic group; commutative automorphic loops; semidirect products; middle nucleus; cyclic groups
UR - http://eudml.org/doc/261987
ER -
References
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- Jedlička P., Kinyon M., Vojtěchovský P., 10.1080/00927870903200877, Comm. Algebra 38 (2010), no. 9, 3243–3267. Zbl1209.20069MR2724218DOI10.1080/00927870903200877
- Jedlička P., Simon D., On commutative A-loops of order , to appear.
- Pflugfelder H.O., Quasigroups and Loops: Introduction, Heldermann, Berlin, 1990. Zbl0715.20043MR1125767
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