Description:
<jats:p>Let <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0008439500053571_inline1" /> be the lower central series of a group G, where K<jats:sub>2</jats:sub>(G) = [G, G] and inductively K<jats:sub>n+1</jats:sub>(G) = [K<jats:sub>n</jats:sub> (G), G]. A theorem of Blackburn ([1], Hilfssatz) states that</jats:p><jats:p>Theorem 1. The exponent of K<jats:sub>n+1</jats:sub> (G)/K<jats:sub>n+2</jats:sub> (G) divides the exponent of K<jats:sub>n</jats:sub> (G)/K<jats:sub>n+1</jats:sub> (G).</jats:p>