Geodesic
Crossed-inverse-property groupoids
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2007), pp. 101-106.

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The (right, left) crossed-inverse-property in groupoids is investigated. It is shown that the class of all crossed-inverse-property groupoids is a variety of quasigroups. Some properties of the right-crossed-property groupoids are established. 
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V. Izbash; N. Labo. Crossed-inverse-property groupoids. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2007), pp. 101-106. https://geodesic-test.mathdoc.fr/item/BASM_2007_2_a8/

[1] Artzy R., “On loops with a special property”, Proc. Amer. Math. Soc., 6 (1955), 448–453 | DOI | MR | Zbl

[2] Belousov V. D., Tsurkan B. V., “Crossed inverse quasigroups ($CI$-quasigroups)”, Izv. Vyssh. Uchebn. Zaved. Math., 1969, no. 3, 21–27 (in Russian) | MR | Zbl

[3] Keedwell A. D., “Crossed-inverse quasigroups with long inverse cycles and applications to cryptography”, Australas. J. Combin., 20 (1969), 241–250 | MR

[4] Izbash V., Labo N., “On crossed-inverse-property groupoids”, Second Conference of the Mathematical Society of the Republic of Moldova, Abstracts (Chisinau, 2004, August 17–19), 181–182