This article is cited in 1 paper

Partial generalization of one of Macdonald's results

D. V. Lytkina

Siberian State University of Telecommunications and Informatics

Abstract: 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 $G$.

Keywords: $p$-группа, коммутант.

UDC: 512.5

MSC: 20D15

Received September 9, 2011, published December 20, 2011