C-loops: An introduction

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dc.creatorPhillips, J. D.
dc.creatorVojtěchovský, Petr
dc.date2007-01-24
dc.date.accessioned2026-07-07T07:42:53Z
dc.date.available2026-07-07T07:42:53Z
dc.descriptionC-loops are loops satisfying $x(y(yz))=((xy)y)z$. They often behave analogously to Moufang loops and they are closely related to Steiner triple systems and combinatorics. We initiate the study of C-loops by proving: (i) Steiner loops are C-loops, (ii) C-loops are alternative, inverse property loops with squares in the nucleus, (iii) the nucleus of a C-loop is a normal subgroup, (iv) C-loops modulo their nucleus are Steiner loops, (v) C-loops are power associative, power alternative but not necessarily diassociative, (vi) torsion commutative C-loops are products of torsion abelian groups and torsion commutative 2-C-loops; and several other results. We also give examples of the smallest nonassociative C-loops, and explore the analogy between commutative C-loops and commutative Moufang loops.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0701711
dc.identifierhttp://arxiv.org/abs/math/0701711
dc.identifierPublicationes Mathematicae Debrecen 68 (2006), nos. 1-2, 115-137
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122611
dc.subjectGroup Theory
dc.subject20N05
dc.titleC-loops: An introduction
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