Geodesic
On the product of a $B$-group and a primary group
Problemy fiziki, matematiki i tehniki, no. 3 (2017), pp. 52-57

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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, primary group, product of subgroups.
Mots-clés : $B$-group 
@article{PFMT_2017_3_a8,
     author = {V. N. Kniahina},
     title = {On the product of a $B$-group and a primary group},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {52--57},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2017_3_a8/}
}
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V. N. Kniahina. On the product of a $B$-group and a primary group. Problemy fiziki, matematiki i tehniki, no. 3 (2017), pp. 52-57. http://geodesic.mathdoc.fr/item/PFMT_2017_3_a8/