Left conjugacy closed loops of nilpotency class two |
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| Authors: | Piroska Csörgő Aleš Drápal |
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| Affiliation: | 1. Dept. of Mathematics, E?tv?s University, Pázmány Péter sétány 1/C, H-1117, Budapest, Hungary
2. Dept. of Mathematics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Rep.
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| Abstract: | Every LCC loop Q with Inn Q abelian is nilpotent class two. A loop Q of nilpotency class two is LCC ? L(x, y) = L(y, x) for all x, y ∈ Q ? ?/Z(Mlt Q) is abelian ? [x, y, z] = [x,z,y] for all x, y, z ∈ Q ? [x, y, z] = [xy, z][x, z]?1 for all x, y, z ∈ Q. All nilpotent LCC loops of order p2 are described, and some of their multiplication groups are computed. |
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