Summary
An RA loop is a (necessarily Moufang) loop whose loop rings in any characteristic are alternative, but not associative. There are seven classes of finite indecomposable RA loops. In this paper, we find the indecomposable subloops and the indecomposable nonabelian groups which can appear inside the loops in each class.
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Chein, O., Goodaire, E. Subloops of indecomposable RA loops. Acta Math Hung 109, 15–31 (2005). https://doi.org/10.1007/s10474-005-0232-9
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DOI: https://doi.org/10.1007/s10474-005-0232-9