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latin square; latin subsquare; overlapping latin subsquares; full product in loops

References:

[1] Dénes J., Hermann P.: **On the product of all elements in a finite group**. Ann. Discrete Math. 15 (1982), 105–109. MR 0772587

[2] Heinrich K., Wallis W.D.: **The maximum number of intercalates in a latin square**. Lecture Notes in Math. 884 (1981), 221–233. DOI 10.1007/BFb0091822 | MR 0641250 | Zbl 0475.05014

[3] McKay B.D., Wanless I.M.: **Most latin squares have many subsquares**. J. Combin. Theory Ser. A 86 (1999), 323–347. DOI 10.1006/jcta.1998.2947 | MR 1685535 | Zbl 0948.05014

[4] Pula K.: **Products of all elements in a loop and a framework for non-associative analogues of the Hall-Paige conjecture**. Electron. J. Combin. 16 (2009), R57. MR 2505099

[5] Ryser H.J.: **A combinatorial theorem with an application to latin rectangles**. Proc. Amer. Math. Soc. 2 (1951), 550–552. DOI 10.1090/S0002-9939-1951-0042361-0 | MR 0042361 | Zbl 0043.01202

[6] van Rees G.H.J.: **Subsquares and transversals in latin squares**. Ars Combin. 29B (1990), 193–204. MR 1412875 | Zbl 0718.05014