Dokažemo, da če je ▫$G$▫ končna grupa, potem eksponent njenega multiplikatorja Bogomolova deli eksponent grupe ▫$G$▫ v naslednjih primerih: (i) ▫$G$▫ je meta abelova, (ii) ▫$\exp G=4$▫, (iii) ▫$G$▫ ...je nilpotentna razreda ▫$\le 5$▫, (iv) ▫$G$▫ je 4-Engelova grupa.
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