Geodesic
Partial generalization of one of Macdonald's results
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 369-371

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It is proved that if in every finite subgroup of a $2$-group $G$ the identity $[x,y]^2=1$ holds, then this identity holds in $G$ also. In particular, $G$ is locally finite, its derived subgroup is of exponent 4, and the second derived subgroup belongs to the center of $G$.
Mots-clés : $p$-группа, коммутант. 
@article{SEMR_2011_8_a30,
     author = {D. V. Lytkina},
     title = {Partial generalization of one of {Macdonald's} results},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {369--371},
     publisher = {mathdoc},
     volume = {8},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2011_8_a30/}
}
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D. V. Lytkina. Partial generalization of one of Macdonald's results. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 369-371. http://geodesic.mathdoc.fr/item/SEMR_2011_8_a30/