Geodesic
Normal subgroups of biprimary groups
Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 877-886 
V. S. Monakhov. Normal subgroups of biprimary groups. Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 877-886. http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a9/
@article{MZM_1975_18_6_a9,
     author = {V. S. Monakhov},
     title = {Normal subgroups of biprimary groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {877--886},
     year = {1975},
     volume = {18},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that, except for three cases, a soluble group of order $p^\alpha m$, $p^\alpha>m$, always contains a nontrivial normal $p$-subgroup. Examples are constructed to show that in the excluded cases, nontrivial normal $p$-subgroups may not exist.