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The group of continuous autotopisms of the loop \(S^ 7\). (Die Gruppe der stetigen Autotopismen des Loops \(S^ 7\).) (German) Zbl 0798.20060

The unit sphere \(S^ 7\) is a subloop of the multiplicative Moufang loop of the eight-dimensional Cayley algebra \(A\). The author considers continuous pseudoautomorphisms and continuous autotopisms of \(S^ 7\). They are shown to be restrictions of corresponding transformations of \(A\). This yields a description of the related groups.
Reviewer: T.Kepka (Praha)

MSC:

20N05 Loops, quasigroups
22A30 Other topological algebraic systems and their representations
20E36 Automorphisms of infinite groups
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