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On the loop cloud of a group. (English) Zbl 1434.20053

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
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