On the $p$-length of finite $p$-soluble groups

Finite $p$-soluble groups with maximal subgroups of $p$-length 1 are investigated. It is proved that a finite $p$-soluble group is of $p$-length 1 if its Sylow $p$-subgroup is extraspecial and is isomorphic to a normal Sylow $p$-subgroup of a minimal non-supersoluble group of odd order.