Geodesic
On commutative Moufang loops with some restrictions for subloops and subgroups of its multiplication groups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2009), pp. 52-56.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that if an infinite commutative Moufang loop $L$ has such an infinite subloop $H$ that in $L$ every associative subloop which has with $H$ an infinite intersection is a normal subloop then the loop $L$ is associative. It is also proved that if the multiplication group $\mathfrak M$ of infinite commutative Moufang loop $L$ has such an infinite subgroup $\mathfrak N$ that in $\mathfrak M$ every abelian subgroup which has with $\mathfrak N$ an infinite intersection is a normal subgroup then the loop $L$ is associative. 
@article{BASM_2009_3_a4,
     author = {Natalia Lupashco},
     title = {On commutative {Moufang} loops with some restrictions for subloops and subgroups of its multiplication groups},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {52--56},
     publisher = {mathdoc},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2009_3_a4/}
}
TY  - JOUR
AU  - Natalia Lupashco
TI  - On commutative Moufang loops with some restrictions for subloops and subgroups of its multiplication groups
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2009
SP  - 52
EP  - 56
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2009_3_a4/
LA  - en
ID  - BASM_2009_3_a4
ER  - 
%0 Journal Article
%A Natalia Lupashco
%T On commutative Moufang loops with some restrictions for subloops and subgroups of its multiplication groups
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2009
%P 52-56
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2009_3_a4/
%G en
%F BASM_2009_3_a4
Natalia Lupashco. On commutative Moufang loops with some restrictions for subloops and subgroups of its multiplication groups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2009), pp. 52-56. http://geodesic.mathdoc.fr/item/BASM_2009_3_a4/

[1] Sandu N. I., “Commutative Moufang loops with minimum condition for subloops, I”, Buletinul Academiei de Ştiinţe a Republicii Moldova, Matematica, 2003, no. 3(43), 25–40 | MR

[2] Sandu N. I., “Commutative Moufang loops with minimum condition for subloops, II”, Buletinul Academiei de Ştiinţe a Republicii Moldova, Matematica, 2004, no. 2(45), 33–48 | MR | Zbl

[3] Lupashco N. T., “On commutative Moufang loops with some restrictions for subgroups of its multiplication groups”, Buletinul Academiei de Ştiinţe a Republicii Moldova, Matematica, 2006, no. 2(51), 95–101 | MR | Zbl

[4] Bruck R. H., A survey of binary systems, Springer Verlag, Berlin–Heidelberg, 1958 | MR | Zbl

[5] Norton D., “Hamiltonian loops”, Proc. Amer. Math. Soc., 3 (1952), 56–65 | DOI | MR | Zbl

[6] Sandu N. I., “Centrally nilpotent commutative Moufang loops”, Quasigroups and loops, Mat. Issled., 51, 1979, 145–155 (Russian) | MR | Zbl

[7] Semko N. N., “Some forms of non-abelian groups with given systems of invariant infinite abelian subgroups”, Ukr. mat. jurn., 33:2 (1981), 270–273 (Russian) | MR | Zbl