On Moufang A-loops

Phillips, Jon D.. "On Moufang A-loops." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 371-375. <http://eudml.org/doc/248615>.

@article{Phillips2000,
abstract = {In a series of papers from the 1940’s and 1950’s, R.H. Bruck and L.J. Paige developed a provocative line of research detailing the similarities between two important classes of loops: the diassociative A-loops and the Moufang loops ([1]). Though they did not publish any classification theorems, in 1958, Bruck’s colleague, J.M. Osborn, managed to show that diassociative, commutative A-loops are Moufang ([5]). In [2] we relaunched this now over 50 year old program by examining conditions under which general — not necessarily commutative — diassociative A-loops are, in fact, Moufang. Here, we finish part of the program by characterizing Moufang A-loops. We also investigate simple diassociative A-loops as well as a class of centrally nilpotent diassociative A-loops. These results, in toto, reveal the distinguished positions two familiar classes of diassociative A-loops — namely groups and commutative Moufang loops–play in the general theory.},
author = {Phillips, Jon D.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {diassociative; A-loop; Moufang; diassociative A-loops; commutative A-loops; Moufang A-loops; commutative Moufang loops},
language = {eng},
number = {2},
pages = {371-375},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On Moufang A-loops},
url = {http://eudml.org/doc/248615},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Phillips, Jon D.
TI - On Moufang A-loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 2
SP - 371
EP - 375
AB - In a series of papers from the 1940’s and 1950’s, R.H. Bruck and L.J. Paige developed a provocative line of research detailing the similarities between two important classes of loops: the diassociative A-loops and the Moufang loops ([1]). Though they did not publish any classification theorems, in 1958, Bruck’s colleague, J.M. Osborn, managed to show that diassociative, commutative A-loops are Moufang ([5]). In [2] we relaunched this now over 50 year old program by examining conditions under which general — not necessarily commutative — diassociative A-loops are, in fact, Moufang. Here, we finish part of the program by characterizing Moufang A-loops. We also investigate simple diassociative A-loops as well as a class of centrally nilpotent diassociative A-loops. These results, in toto, reveal the distinguished positions two familiar classes of diassociative A-loops — namely groups and commutative Moufang loops–play in the general theory.
LA - eng
KW - diassociative; A-loop; Moufang; diassociative A-loops; commutative A-loops; Moufang A-loops; commutative Moufang loops
UR - http://eudml.org/doc/248615
ER -