Abstract
Let K be a field, O(K) the split Cayley–Dickson (octonion) algebra over K, and G(K) the Moufang loop formed by all elements of O(K) having norm other than 0. A transvection is an element of G(K) having the form where
and
In the paper, subloops of G(K), containing a subloop which consists only of transvections, are studied.
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2020 MATHEMATICS SUBJECT CLASSIFICATION: