Ealy, Clifton E. jun. On the loop cloud of a group. (English) Zbl 1434.20053 Congr. Numerantium 231, 109-115 (2018). Summary: Informally, a quasigroup with identity, briefly – a loop, is a group without the axiom of associativity. In 1939, Reinhold Baer showed how to obtain a loop as a “factor loop” of a group. In this note, I will define the Loop Cloud of a Group and prove some properties of the Loop Cloud of a group \(G\) and \(G\). For example, \(G\) is a simple group if and only if the loops in the loop cloud of \(G\) are not groups. MSC: 20N05 Loops, quasigroups Keywords:quasigroup with identity; simple groups; coset quasigroups with identity of a group PDFBibTeX XMLCite \textit{C. E. Ealy jun.}, Congr. Numerantium 231, 109--115 (2018; Zbl 1434.20053)