Geodesic
$T$-partitions of quasigroups and groups
Diskretnaya Matematika, Tome 4 (1992) no. 3, pp. 47-56.

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We introduce the concept of a $T$-partition of a quasigroup that generalizes various situations when the Cayley table of a quasigroup can be partitioned into smaller Latin squares. From all the $T$-partitions we identify left-regular [resp. right-regular], regular and homogeneous $T$-partitions. The $T$-partitions of each type of quasigroup form a lattice. We study the lattices of $T$-partitions of groups. In particular, we prove that any finite abelian group can be uniquely reconstructed up to isomorphism from the lattice of its left-regular [resp. right-regular] $T$-partitions. 
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     author = {M. M. Glukhov},
     title = {$T$-partitions of quasigroups and groups},
     journal = {Diskretnaya Matematika},
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     url = {http://geodesic.mathdoc.fr/item/DM_1992_4_3_a2/}
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M. M. Glukhov. $T$-partitions of quasigroups and groups. Diskretnaya Matematika, Tome 4 (1992) no. 3, pp. 47-56. http://geodesic.mathdoc.fr/item/DM_1992_4_3_a2/