The finite embeddability property for IP loops and local embeddability of groups into finite IP loops - Vodička, Martin (Ars mathematica contemporanea, 2019)
We prove that the class of all loops with the inverse property (IP loops) has the Finite Embeddability Property (FEP). As a consequence, every group is locally embeddable into finite IP loops. The first one of these results is obtained as a consequence of a more general embeddability theorem, contributing to a list of problems posed by T. Evans in 1978, namely, that every finite partial IP loop can be embedded into a finite IP loop.
Keywords: 2-factorizations; finite embeddability property; group; grupa; IP loop; IP zanka; končna vložitvena lastnost; local embeddability; lokalna vložljivost