On automorphisms of commutative Moufang loops
Diskretnaya Matematika, Tome 23 (2011) no. 2, pp. 108-114.

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It is proved that the automorphism group of any commutative Moufang loop $Q$ is an extension of the group $F(1)$ consisting of all automorphisms of the loop $Q$ which induce the identity mapping onto the factor-loop $Q/A(Q)$ of $Q$ by means of the automorphism group of the abelian group $Q/A(Q)$. We investigate the structure of the group $F(1)$ in the cases where the loop $Q$ is either centrally nilpotent, or finitely generated, or is a $ZA$-loop.
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N. T. Lupasço. On automorphisms of commutative Moufang loops. Diskretnaya Matematika, Tome 23 (2011) no. 2, pp. 108-114. http://geodesic.mathdoc.fr/item/DM_2011_23_2_a9/

[1] Sandu N. I., “Ob otnositelno svobodnykh kommutativnykh lupakh Mufang”, Algebra i logika, 18:3 (1979), 194–205 | MR | Zbl

[2] Sandu N. I., “Medialno nilpotentnye distributivnye kvazigruppy i SN-kvazigruppy”, Sibirskii matem. zh., 28:2 (1987), 159–170 | MR | Zbl

[3] Bruck R. H., Survey of binary systems, Springer, Berlin, 1958 | MR | Zbl

[4] Smith J. D. H., “On the nilpotence class of commutative Moufang loops”, Math. Proc. Cambridge Phil. Soc., 84:3 (1978), 387–404 | DOI | MR | Zbl

[5] Malbos J.-P., “Sur la classe de nilpotence des boucles commutatives de Moufang et des espaces mediaux”, C. R. Acad. Sci. Paris Sér. A, 287 (1978), 691–693 | MR | Zbl

[6] Beneteau L., “Free commutative Moufang loops and anticommutative graded rings”, J. Algebra, 67 (1980), 1–35 | DOI | MR | Zbl

[7] Sandu N. I., “O dline nizhnego tsentralnogo ryada (proizvodnogo ryada) kommutativnoi lupy Mufang”, Matematicheskie zametki, 62:3 (1997), 475–478 | MR | Zbl

[8] Sandu N. I., “O tsentralno nilpotentnykh kommutativnykh lupakh Mufang”, Kvazigruppy i lupy, Shtiintsa, Kishinev, 1979, 145–155 | MR

[9] Maltsev A. I., “O nekotorykh klassakh beskonechnykh razreshimykh grupp”, Matematicheskii sb., 28(70):3 (1951), 567–588 | MR | Zbl

[10] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, Moskva, 1977 | MR | Zbl

[11] Evans T., “Identities and relations in commutative Moufang loops”, J. Algebra, 31 (1974), 508–513 | DOI | MR | Zbl