Enumeration of nilpotent loops up to isotopy
Commentationes Mathematicae Universitatis Carolinae (2012)
- Volume: 53, Issue: 2, page 159-177
- ISSN: 0010-2628
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topClavier, Lucien. "Enumeration of nilpotent loops up to isotopy." Commentationes Mathematicae Universitatis Carolinae 53.2 (2012): 159-177. <http://eudml.org/doc/247109>.
@article{Clavier2012,
abstract = {We modify tools introduced in [Daly D., Vojtěchovský P., Enumeration of nilpotent loops via cohomology, J. Algebra 322 (2009), no. 11, 4080–4098] to count, for any odd prime $q$, the number of nilpotent loops of order $2q$ up to isotopy, instead of isomorphy.},
author = {Clavier, Lucien},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; nilpotent; enumeration; cohomology; isomorphy; isotopy; finite loops; numbers of nilpotent loops; loop cohomology groups; numbers of isotopism classes; isotopies; central extensions; loop cocycles},
language = {eng},
number = {2},
pages = {159-177},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Enumeration of nilpotent loops up to isotopy},
url = {http://eudml.org/doc/247109},
volume = {53},
year = {2012},
}
TY - JOUR
AU - Clavier, Lucien
TI - Enumeration of nilpotent loops up to isotopy
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 2
SP - 159
EP - 177
AB - We modify tools introduced in [Daly D., Vojtěchovský P., Enumeration of nilpotent loops via cohomology, J. Algebra 322 (2009), no. 11, 4080–4098] to count, for any odd prime $q$, the number of nilpotent loops of order $2q$ up to isotopy, instead of isomorphy.
LA - eng
KW - loop; nilpotent; enumeration; cohomology; isomorphy; isotopy; finite loops; numbers of nilpotent loops; loop cohomology groups; numbers of isotopism classes; isotopies; central extensions; loop cocycles
UR - http://eudml.org/doc/247109
ER -
References
top- Clavier L., About the autotopisms of abelian groups, 2012, http://arxiv.org/abs/1201.5655.
- Daly D., Vojtěchovský P., 10.1016/j.jalgebra.2009.03.042, J. Algebra 322 (2009), no. 11, 4080–4098. Zbl1209.20068MR2556139DOI10.1016/j.jalgebra.2009.03.042
- Pflugfelder H.O., Quasigroups and Loops: Introduction, Heldermann, Berlin, 1990. Zbl0715.20043MR1125767
- Phillips J.D., Vojtěchovský P., 10.1007/s00012-005-1941-1, Algebra Universalis 54 (2005), no. 3, 259–271. Zbl1102.20054MR2219409DOI10.1007/s00012-005-1941-1
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