Structural interactions of conjugacy closed loops |
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Authors: | Ales Drá pal |
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Institution: | Department of Mathematics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic |
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Abstract: | We study conjugacy closed loops by means of their multiplication groups. Let be a conjugacy closed loop, its nucleus, the associator subloop, and and the left and right multiplication groups, respectively. Put . We prove that the cosets of agree with orbits of , that and that one can define an abelian group on . We also explain why the study of finite conjugacy closed loops can be restricted to the case of nilpotent. Group is shown to be a subgroup of a power of (which is abelian), and we prove that can be embedded into . Finally, we describe all conjugacy closed loops of order . |
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Keywords: | Conjugacy closed loop multiplication group nucleus |
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