The paper surveys the known results concerning the question: ``For what values of $n$ does there exist a nonassociative Moufang loop of order $n$?'' Proofs of the newest results for $n$ odd, and a complete resolution of the case $n$ even are also presented.
@article{119159, author = {Orin Chein and Andrew Rajah}, title = {Possible orders of nonassociative Moufang loops}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {41}, year = {2000}, pages = {237-244}, zbl = {1038.20045}, mrnumber = {1780867}, language = {en}, url = {http://dml.mathdoc.fr/item/119159} }
Chein, Orin; Rajah, Andrew. Possible orders of nonassociative Moufang loops. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 237-244. http://gdmltest.u-ga.fr/item/119159/
Gewebe und Gruppen, Math. Ann. 114 (1937), 414-431. (1937) | MR 1513147 | Zbl 0016.22603
Contributions to the theory of loops, Trans. Amer. Math. Soc. 60 (1946), 245-354. (MR 8, p.134). (1946) | MR 0017288 | Zbl 0061.02201
A Survey of Binary Systems, Ergeb. Math. Grenzgeb., vol. 20, Springer Verlag, 1968. (MR 20 # 76). | MR 0093552 | Zbl 0141.01401
Moufang loops of small order. I, Trans. Amer. Math. Soc. 188 (1974), 31-51. (MR 48 # 8673). (1974) | MR 0330336 | Zbl 0286.20088
Moufang loops of small order, Mem. Amer. Math. Soc. 197 , Vol 13, Issue 1 (1978), 1-131. (MR 57 # 6271). (1978) | MR 0466391 | Zbl 0378.20053
The smallest Moufang loop, Archiv der Mathematik 22 (1971), 573-576. (MR 45 # 6966). (1971) | MR 0297914 | Zbl 0241.20061
On loops of odd order II, J. Algebra 8 (1968), 393-414. (MR 36 # 5250). (1968) | MR 0222198 | Zbl 0155.03901
Moufang loops of order $p^{4}$, Nanta Math. 7 (1974), 33-34. (MR 51 # 5826). (1974) | MR 0369593
On Moufang loops of odd order $pq^{2}$, J. Algebra 176 (1995), 265-270. (MR 96i # 20082). (1995) | MR 1345304
Moufang loops of odd order $p_{1}^{2}p_{2}^{2}...p_m^{2}$, J. Algebra 181 (1996), 876-883 (MR 97i # 20083). (1996) | MR 1386583
Moufang loops of odd order $p^{4}q_{1}...q_n$, J. Algebra 184 (1996), 561-569. (MR 97k # 20118). (1996) | MR 1409228 | Zbl 0860.20054
Moufang loops of odd order $p^{\alpha }q_{1}^{2}...q_n^{2}r_{1}...r_m$, J. Algebra 190 (1997), 474-486. (MR 98b # 20115). (1997) | MR 1441958 | Zbl 0874.20046
Moufang loops of orders $2pq$, Bull. of the Malaysian Math. Soc. 15 (1992), 27-29. (MR 93j # 20142). (1992) | MR 1196349 | Zbl 0766.20025
Moufang loops of even order, J. Algebra 164 (1994), 409-414. (MR 95b # 20097). (1994) | MR 1271244 | Zbl 0804.20050
Moufang loops of odd order $p^mq_{1}...q_n$, J. Algebra 168 (1994), 348-352. (MR 95g # 20068). (1994) | MR 1289104 | Zbl 0814.20054
On Moufang loops of order the product of three primes, J. Algebra 112 (1988), 122-128. (MR 89c # 20120). (1988) | MR 0921968
Corrigendum, J. Algebra 145 (1992), p.262. (MR 92j # 20066). (1992) | MR 1144674 | Zbl 0742.20068
Which Moufang loops are associative, Doctoral Dissertation, University Sains Malaysia, 1996. | Zbl 1006.20501
Moufang loops of order $2m$, Publ. Math. Debrecen 55 (1999), 47-51. (1999) | MR 1708430 | Zbl 0933.20053
Group Theory, Prentice Hall, Englewood Cliffs, NJ, 1964. | MR 0167513 | Zbl 0897.20029
Nilpotency conditions for finite loops, Illinois J. Math. 9 (1965), 399-409. (MR 31 # 5918). (1965) | MR 0181691 | Zbl 0135.03701
The theory of alternative rings, Hamb. Abhandl. 8 (1930), 123-147. (1930)