Geodesic
Varieties in which all finite groups are Abelian
Sbornik. Mathematics, Tome 54 (1986) no. 1, pp. 57-80 
A. Yu. Ol'shanskii. Varieties in which all finite groups are Abelian. Sbornik. Mathematics, Tome 54 (1986) no. 1, pp. 57-80. http://geodesic.mathdoc.fr/item/SM_1986_54_1_a2/
@article{SM_1986_54_1_a2,
     author = {A. Yu. Ol'shanskii},
     title = {Varieties in which all finite groups are {Abelian}},
     journal = {Sbornik. Mathematics},
     pages = {57--80},
     year = {1986},
     volume = {54},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_54_1_a2/}
}
TY  - JOUR
AU  - A. Yu. Ol'shanskii
TI  - Varieties in which all finite groups are Abelian
JO  - Sbornik. Mathematics
PY  - 1986
SP  - 57
EP  - 80
VL  - 54
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1986_54_1_a2/
LA  - en
ID  - SM_1986_54_1_a2
ER  - 
%0 Journal Article
%A A. Yu. Ol'shanskii
%T Varieties in which all finite groups are Abelian
%J Sbornik. Mathematics
%D 1986
%P 57-80
%V 54
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1986_54_1_a2/
%G en
%F SM_1986_54_1_a2

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

The well-known problem of the existence of a variety that contains non-Abelian groups, but in which all finite groups are Abelian, is solved affirmatively. The variety $\mathfrak M$ is given by a single two-variable identity. For the proof, the author inductively introduces defining relations for $\mathfrak M$-free groups. In the study of their consequences, he uses a geometrical interpretation for deduction. The exposition is heavily dependent on a previous paper of the author. Figures: 4. Bibliography: 7 titles.

[1] Miller G. A., Moreno H. C., “Non-abelian groups in which every subgroup is abelian”, Trans. Amer. Math. Soc., 4:4 (1903), 398–404 | DOI | MR | Zbl

[2] Hall Ph., “On the finiteness of certain soluble groups”, Proc. London Math. Soc., 9 (1959), 595–622 | DOI | MR | Zbl

[3] Neimakh Kh., Mnogoobraziya grupp, Mir, M., 1969 | MR

[4] Kourovskaya tetrad: Nereshennye voprosy teorii grupp, Novosibirsk, 1973

[5] Olshanskii A. Yu., “Gruppy ogranichennogo perioda s podgruppami prostogo poryadka”, Algebra i logika, 21:5 (1982), 553–618 | MR

[6] Kharari F., Teoriya grafov, Mir, M., 1973 | MR

[7] Olshanskii A. Yu., “O teoreme Novikova–Adyana”, Matem. sb., 118(160) (1982), 203–235 | MR