Relatives of K-loops: Theory and examples

Hubert Kiechle

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 2, page 301-323
  • ISSN: 0010-2628

Abstract

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A K-loop or Bruck loop is a Bol loop with the automorphic inverse property. An overview of the most important theorems on K-loops and some of their relatives, especially Kikkawa loops, is given. First, left power alternative loops are discussed, then Kikkawa loops are considered. In particular, their nuclei are determined. Then the attention is paid to general K-loops and some special classes of K-loops such as 2-divisible ones. To construct examples, the method of derivation is introduced. This has been used in the past to construct quasifields from fields. Many known methods to constructing loops can be seen as special cases of derivations. The examples given show the independence of various axioms.

How to cite

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Kiechle, Hubert. "Relatives of K-loops: Theory and examples." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 301-323. <http://eudml.org/doc/248626>.

@article{Kiechle2000,
abstract = {A K-loop or Bruck loop is a Bol loop with the automorphic inverse property. An overview of the most important theorems on K-loops and some of their relatives, especially Kikkawa loops, is given. First, left power alternative loops are discussed, then Kikkawa loops are considered. In particular, their nuclei are determined. Then the attention is paid to general K-loops and some special classes of K-loops such as 2-divisible ones. To construct examples, the method of derivation is introduced. This has been used in the past to construct quasifields from fields. Many known methods to constructing loops can be seen as special cases of derivations. The examples given show the independence of various axioms.},
author = {Kiechle, Hubert},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {K-loop; Bol loop; Kikkawa loop; left power alternative loop; 2-divisible loop; derivation; K-loops; Bol loops; Kikkawa loops; left power alternative loops; 2-divisible loops; derivations},
language = {eng},
number = {2},
pages = {301-323},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Relatives of K-loops: Theory and examples},
url = {http://eudml.org/doc/248626},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Kiechle, Hubert
TI - Relatives of K-loops: Theory and examples
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 2
SP - 301
EP - 323
AB - A K-loop or Bruck loop is a Bol loop with the automorphic inverse property. An overview of the most important theorems on K-loops and some of their relatives, especially Kikkawa loops, is given. First, left power alternative loops are discussed, then Kikkawa loops are considered. In particular, their nuclei are determined. Then the attention is paid to general K-loops and some special classes of K-loops such as 2-divisible ones. To construct examples, the method of derivation is introduced. This has been used in the past to construct quasifields from fields. Many known methods to constructing loops can be seen as special cases of derivations. The examples given show the independence of various axioms.
LA - eng
KW - K-loop; Bol loop; Kikkawa loop; left power alternative loop; 2-divisible loop; derivation; K-loops; Bol loops; Kikkawa loops; left power alternative loops; 2-divisible loops; derivations
UR - http://eudml.org/doc/248626
ER -

References

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