Moufang semidirect products of loops with groups and inverse property extensions

Mark Greer; Lee Raney

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 3, page 411-420
  • ISSN: 0010-2628

Abstract

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We investigate loops which can be written as the semidirect product of a loop and a group, and we provide a necessary and sufficient condition for such a loop to be Moufang. We also examine a class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms on an inverse property loop. In particular, we consider closure properties of certain extensions similar to those as in [S. Gagola III, Cyclic extensions of Moufang loops induced by semiautomorphisms, J. Algebra Appl. 13 (2014), no. 4, 1350128], but from an external point of view.

How to cite

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Greer, Mark, and Raney, Lee. "Moufang semidirect products of loops with groups and inverse property extensions." Commentationes Mathematicae Universitatis Carolinae 55.3 (2014): 411-420. <http://eudml.org/doc/261866>.

@article{Greer2014,
abstract = {We investigate loops which can be written as the semidirect product of a loop and a group, and we provide a necessary and sufficient condition for such a loop to be Moufang. We also examine a class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms on an inverse property loop. In particular, we consider closure properties of certain extensions similar to those as in [S. Gagola III, Cyclic extensions of Moufang loops induced by semiautomorphisms, J. Algebra Appl. 13 (2014), no. 4, 1350128], but from an external point of view.},
author = {Greer, Mark, Raney, Lee},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {extensions; semidirect products; Moufang loops; inverse property loops; Moufang loops; semidirect products; inverse property loops; loop extensions},
language = {eng},
number = {3},
pages = {411-420},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Moufang semidirect products of loops with groups and inverse property extensions},
url = {http://eudml.org/doc/261866},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Greer, Mark
AU - Raney, Lee
TI - Moufang semidirect products of loops with groups and inverse property extensions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 3
SP - 411
EP - 420
AB - We investigate loops which can be written as the semidirect product of a loop and a group, and we provide a necessary and sufficient condition for such a loop to be Moufang. We also examine a class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms on an inverse property loop. In particular, we consider closure properties of certain extensions similar to those as in [S. Gagola III, Cyclic extensions of Moufang loops induced by semiautomorphisms, J. Algebra Appl. 13 (2014), no. 4, 1350128], but from an external point of view.
LA - eng
KW - extensions; semidirect products; Moufang loops; inverse property loops; Moufang loops; semidirect products; inverse property loops; loop extensions
UR - http://eudml.org/doc/261866
ER -

References

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