Abstract
A subloop of a loop Q is said to be normal if it is stabilized by all maps in the inner mapping group of Q. Here we show that in many cases, the inner mapping group of a Moufang loop is actually generated by conjugation maps. This includes any Moufang loop whose cubes generate either the entire loop or a subloop of index three. Such a result can be an extremely useful tool when proving that certain subloops are indeed normal just by showing that they are stabilized by the conjugation maps.
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Gagola, S.M. When are inner mapping groups generated by conjugation maps?. Arch. Math. 101, 207–212 (2013). https://doi.org/10.1007/s00013-013-0561-9
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DOI: https://doi.org/10.1007/s00013-013-0561-9