On finite commutative loops which are centrally nilpotent

Emma Leppälä; Markku Niemenmaa

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 2, page 139-143
  • ISSN: 0010-2628

Abstract

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Let Q be a finite commutative loop and let the inner mapping group I ( Q ) ≅ C p n × C p n , where p is an odd prime number and n ≥ 1 . We show that Q is centrally nilpotent of class two.

How to cite

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Leppälä, Emma, and Niemenmaa, Markku. "On finite commutative loops which are centrally nilpotent." Commentationes Mathematicae Universitatis Carolinae 56.2 (2015): 139-143. <http://eudml.org/doc/270112>.

@article{Leppälä2015,
abstract = {Let $Q$ be a finite commutative loop and let the inner mapping group $I(Q) \cong C_\{p^n\} \times C_\{p^n\}$, where $p$ is an odd prime number and $n \ge 1$. We show that $Q$ is centrally nilpotent of class two.},
author = {Leppälä, Emma, Niemenmaa, Markku},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; inner mapping group; centrally nilpotent loop; finite commutative loops; Bol loops; Moufang loops; autotopisms; pseudoautomorphisms; inner mapping groups; centrally nilpotent loops; connected transversals},
language = {eng},
number = {2},
pages = {139-143},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On finite commutative loops which are centrally nilpotent},
url = {http://eudml.org/doc/270112},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Leppälä, Emma
AU - Niemenmaa, Markku
TI - On finite commutative loops which are centrally nilpotent
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 2
SP - 139
EP - 143
AB - Let $Q$ be a finite commutative loop and let the inner mapping group $I(Q) \cong C_{p^n} \times C_{p^n}$, where $p$ is an odd prime number and $n \ge 1$. We show that $Q$ is centrally nilpotent of class two.
LA - eng
KW - loop; inner mapping group; centrally nilpotent loop; finite commutative loops; Bol loops; Moufang loops; autotopisms; pseudoautomorphisms; inner mapping groups; centrally nilpotent loops; connected transversals
UR - http://eudml.org/doc/270112
ER -

References

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  1. Bruck R.H., 10.1090/S0002-9947-1946-0017288-3, Trans. Amer. Math. Soc. 60 (1946), 245–354. Zbl0061.02201MR0017288DOI10.1090/S0002-9947-1946-0017288-3
  2. Csörgö P., 10.1016/j.ejc.2005.12.002, European J. Combin. 28 (2007), 858–867. Zbl1149.20053MR2300766DOI10.1016/j.ejc.2005.12.002
  3. Drápal A., Vojtěchovský P., 10.1016/j.ejc.2007.10.001, European J. Combin. 29 (2008), no. 7, 1662–1681. MR2431758DOI10.1016/j.ejc.2007.10.001
  4. Kepka T., Niemenmaa M., 10.1007/BF01198806, Arch. Math. 60 (1993), 233–236. MR1201636DOI10.1007/BF01198806
  5. Niemenmaa M., 10.1017/S0004972700038491, Bull. Austral. Math. Soc. 71 (2005), 487–492. Zbl1080.20061MR2150938DOI10.1017/S0004972700038491
  6. Niemenmaa M., Kepka T., 10.1016/0021-8693(90)90152-E, J. Algebra 135 (1990), 112–122. Zbl0706.20046MR1076080DOI10.1016/0021-8693(90)90152-E
  7. Niemenmaa M., Kepka T., 10.1017/S0004972700016166, Bull. Austral. Math. Soc. 49 (1994), 121–128. Zbl0799.20020MR1262682DOI10.1017/S0004972700016166
  8. Niemenmaa M., Rytty M., Connected transversals and multiplication groups of loops, Quasigroups and Related Systems 15 (2007), 95–107. Zbl1133.20009MR2379127

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