Abstract.
Several new tools are developed dealing with multiplication groups of loops. One of them is based upon the theorem that the inner mapping group of a loop never acts faithfully on any of its orbits, unless it is trivial. The applications include an analysis of loops whose inner mapping group is nonabelian of order pq. Some important earlier results are proved anew in a shorter way.
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(Received 5 March 2001; in revised form 11 June 2001)
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Drápal, A. Orbits of Inner Mapping Groups. Mh Math 134, 191–206 (2002). https://doi.org/10.1007/s605-002-8256-2
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DOI: https://doi.org/10.1007/s605-002-8256-2