Group conjugation has non-trivial LD-identities

Aleš Drápal; Tomáš Kepka; Michal Musílek

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 2, page 219-222
  • ISSN: 0010-2628

Abstract

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We show that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.

How to cite

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Drápal, Aleš, Kepka, Tomáš, and Musílek, Michal. "Group conjugation has non-trivial LD-identities." Commentationes Mathematicae Universitatis Carolinae 35.2 (1994): 219-222. <http://eudml.org/doc/247632>.

@article{Drápal1994,
abstract = {We show that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.},
author = {Drápal, Aleš, Kepka, Tomáš, Musílek, Michal},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {left distributivity; free group; identity; group conjugation; subvariety of left distributive idempotent groupoids; cancellative left distributive groupoids},
language = {eng},
number = {2},
pages = {219-222},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Group conjugation has non-trivial LD-identities},
url = {http://eudml.org/doc/247632},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Drápal, Aleš
AU - Kepka, Tomáš
AU - Musílek, Michal
TI - Group conjugation has non-trivial LD-identities
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 2
SP - 219
EP - 222
AB - We show that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.
LA - eng
KW - left distributivity; free group; identity; group conjugation; subvariety of left distributive idempotent groupoids; cancellative left distributive groupoids
UR - http://eudml.org/doc/247632
ER -

References

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  1. Dehornoy P., Braid groups and left distributive structures, Transactions AMS, to appear. 
  2. Kepka T., Notes on left distributive groupoids, Acta Univ. Carolinae - Math. et Ph. 22 (1981), 23-37. (1981) Zbl0517.20048MR0654379
  3. Laver R., The left distributive law and the freeness of an algebra of elementary embeddings, Advances in Mathematics 91 (1992), 209-231. (1992) Zbl0822.03030MR1149623
  4. Pierce R.S., Symmetric groupoids, Osaka J. Math. 15 (1978), 51-76. (1978) Zbl0395.20033MR0480780
  5. Larue D.M., [unknown], Unpublished notes, 1992. Zbl1106.76319
  6. Larue D.M., [unknown], Ph. D. Thesis University of Colorado, 1994. Zbl1106.76319

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