Normality, nuclear squares and Osborn identities

Aleš Drápal; Michael Kinyon

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 4, page 481-500
  • ISSN: 0010-2628

Abstract

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Let Q be a loop. If S ≤ Q is such that ϕ ( S ) ⊆ S for each standard generator of  Inn Q , then S does not have to be a normal subloop. In an LC loop the left and middle nucleus coincide and form a normal subloop. The identities of Osborn loops are obtained by applying the idea of nuclear identification, and various connections of Osborn loops to Moufang and CC loops are discussed. Every Osborn loop possesses a normal nucleus, and this nucleus coincides with the left, the right and the middle nucleus. Loops that are both Buchsteiner and Osborn are characterized as loops in which each square is in the nucleus.

How to cite

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Drápal, Aleš, and Kinyon, Michael. "Normality, nuclear squares and Osborn identities." Commentationes Mathematicae Universitatis Carolinae 61.4 (2020): 481-500. <http://eudml.org/doc/297349>.

@article{Drápal2020,
abstract = {Let $Q$ be a loop. If $S\le Q$ is such that $\varphi (S) \subseteq S$ for each standard generator of  Inn$\,Q$, then $S$ does not have to be a normal subloop. In an LC loop the left and middle nucleus coincide and form a normal subloop. The identities of Osborn loops are obtained by applying the idea of nuclear identification, and various connections of Osborn loops to Moufang and CC loops are discussed. Every Osborn loop possesses a normal nucleus, and this nucleus coincides with the left, the right and the middle nucleus. Loops that are both Buchsteiner and Osborn are characterized as loops in which each square is in the nucleus.},
author = {Drápal, Aleš, Kinyon, Michael},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; normal subloop; LC loop; Buchsteiner loop; Osborn loop; nuclear identification},
language = {eng},
number = {4},
pages = {481-500},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Normality, nuclear squares and Osborn identities},
url = {http://eudml.org/doc/297349},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Drápal, Aleš
AU - Kinyon, Michael
TI - Normality, nuclear squares and Osborn identities
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 4
SP - 481
EP - 500
AB - Let $Q$ be a loop. If $S\le Q$ is such that $\varphi (S) \subseteq S$ for each standard generator of  Inn$\,Q$, then $S$ does not have to be a normal subloop. In an LC loop the left and middle nucleus coincide and form a normal subloop. The identities of Osborn loops are obtained by applying the idea of nuclear identification, and various connections of Osborn loops to Moufang and CC loops are discussed. Every Osborn loop possesses a normal nucleus, and this nucleus coincides with the left, the right and the middle nucleus. Loops that are both Buchsteiner and Osborn are characterized as loops in which each square is in the nucleus.
LA - eng
KW - loop; normal subloop; LC loop; Buchsteiner loop; Osborn loop; nuclear identification
UR - http://eudml.org/doc/297349
ER -

References

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