References [Art15] Artic, K., On conjugacy closed loops and conjugacy closed loop folders, Ph.D. thesis, RWTH Aachen University (2015). [Art59] Artzy, R., On automorphic-inverse properties in loops, Proc. Amer. Math. Soc., 10 (1959), 588–591. [Bru58] Bruck, R. H., A survey of binary systems, Springer Verlag, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge, Heft 20. Reihe: Gruppentheorie, Berlin (1958), viii+185 pages. [BP56] Bruck, R. H. and Paige, L. J., Loops whose inner mappings are automorphisms, Ann. of Math. (2), 63 (1956), 308–323. [CR99] Colbourn, C. J. and Rosa, A., Triple systems, The Clarendon Press Oxford University Press, Oxford Mathematical Monographs, New York (1999), xvi+560 pages. [CD05] Csörgő, P. and Drápal, A., Left conjugacy closed loops of nilpotency class two, Results Math., 47, 3-4 (2005), 242–265. [DV09] Daly, D. and Vojtěchovský, P., Enumeration of nilpotent loops via cohomology, J. Algebra, 322, 11 (2009), 4080–4098. [BGV12] De Barros, D. A. S., Grishkov, A. and Vojtěchovský, P., Commutative automorphic loops of order p^3, J. Algebra Appl., 11, 5 (2012), 1250100, 15. [Drá03] Drápal, A., Cyclic and dihedral constructions of even order, Comment. Math. Univ. Carolin., 44, 4 (2003), 593–614. [DV06] Drápal, A. and Vojtěchovský, P., Moufang loops that share associator and three quarters of their multiplication tables, Rocky Mountain J. Math., 36, 2 (2006), 425–455. [Fen69] Fenyves, F., Extra loops. II. On loops with identities of Bol-Moufang type, Publ. Math. Debrecen, 16 (1969), 187–192. [GMR99] Goodaire, E. G., May, S. and Raman, M., The Moufang loops of order less than 64, Nova Science Publishers Inc., Commack, NY (1999), xviii+287 pages. [GKN14] Grishkov, A., Kinyon, M. and Nagy, G. P., Solvability of commutative automorphic loops, Proc. Amer. Math. Soc., 142, 9 (2014), 3029–3037. [JM96] Jacobson, M. T. and Matthews, P., Generating uniformly distributed random Latin squares, J. Combin. Des., 4, 6 (1996), 405–437. [JKV12] Jedlička, P., Kinyon, M. and Vojtěchovský, P., Nilpotency in automorphic loops of prime power order, J. Algebra, 350 (2012), 64–76. [JKNV11] Johnson, K. W., Kinyon, M. K., Nagy, G. P. and Vojtěchovský, P., Searching for small simple automorphic loops, LMS J. Comput. Math., 14 (2011), 200–213. [KKP02] Kinyon, M. K., Kunen, K. and Phillips, J. D., Every diassociative A-loop is Moufang, Proc. Amer. Math. Soc., 130, 3 (2002), 619–624. [KKPV16] Kinyon, M. K., Kunen, K., Phillips, J. D. and Vojtěchovský, P., The structure of automorphic loops, Trans. Amer. Math. Soc., 368, 12 (2016), 8901–8927. [KNV15] Kinyon, M. K., Nagy, G. P. and Vojtěchovský, P., Bol loops and Bruck loops of order pq,  (2015), ((preprint)). [Kun00] Kunen, K., The structure of conjugacy closed loops, Trans. Amer. Math. Soc., 352, 6 (2000), 2889–2911. [Lie87] Liebeck, M. W., The classification of finite simple Moufang loops, Math. Proc. Cambridge Philos. Soc., 102, 1 (1987), 33–47. [Moo] Moorhouse, G. E., Bol loops of small order, ((http://www.uwyo.edu/moorhouse/pub/bol/)). [NV03] Nagy, G. P. and Vojtěchovský, P., Octonions, simple Moufang loops and triality, Quasigroups Related Systems, 10 (2003), 65–94. [NV07] Nagy, G. P. and Vojtěchovský, P., The Moufang loops of order 64 and 81, J. Symbolic Comput., 42, 9 (2007), 871–883. [Pfl90] Pflugfelder, H. O., Quasigroups and loops: introduction, Heldermann Verlag, Sigma Series in Pure Mathematics, 7, Berlin (1990), viii+147 pages. [PV05] Phillips, J. D. and Vojtěchovský, P., The varieties of loops of Bol-Moufang type, Algebra Universalis, 54, 3 (2005), 259–271. [SZ12] Slattery, M. and Zenisek, A., Moufang loops of order 243, Commentationes Mathematicae Universitatis Carolinae, 53, 3 (2012), 423–428. [Voj06] Vojtěchovský, P., Toward the classification of Moufang loops of order 64, European J. Combin., 27, 3 (2006), 444–460. [Voj15] Vojtěchovský, P., Three lectures on automorphic loops, Quasigroups Related Systems, 23, 1 (2015), 129–163. [WJ75] Wilson Jr., R. L., Quasidirect products of quasigroups, Comm. Algebra, 3, 9 (1975), 835–850.