This article is cited in 5 papers

MATHEMATICS

On the product of a $B$-group and a primary group

V. N. Kniahina

F. Scorina Gomel State University

Abstract: A finite non-nilpotent group $G$ is called a $B$-group if every proper subgroup of the quotient group $G/\Phi(G)$ is nilpotent. The main properties of $B$-groups are established and the group factorized by a primary and a $B$-group is studied. In particular, it is proved that if $G=HK$ is the product of a $B$-subgroup $H$ with a primary subgroup $K$, and if the order of the non-normal Sylow subgroup of $H$ is not equal to $3$ or $7$, then $G$ is solvable.

Keywords: finite group, $B$-group, primary group, product of subgroups.

UDC: 512.542

Received: 14.06.2017