MATHEMATICS

On the $p$-length of a product of two $B$-groups

V. N. Kniahina

Francisk Skorina Gomel State University

Abstract: A finite non-nilpotent group is called a $B$-group if every proper subgroup of its quotient group by Frattini subgroup is primary. The $p$-length $l_p(G)$ of a finite $p$-soluble group, which is the product of two $B$-subgroups, is studied. It has been proved that $l_p(G)\leqslant 1$ if $p$ does not divide the index of one of the $B$-subgroups.

Keywords: finite group, $B$-group, $p$-soluble group, $p$-length, product of subgroups.

UDC: 512.542

Received: 13.06.2024

DOI: 10.54341/20778708_2024_4_61_48