@article {BrKoSt2005,
 author="R.M. Bryant, L.G. Kov\'acs and Ralph St\"ohr",
 title={Subalgebras of free restricted Lie algebras},
 journal="Bull. Austral. Math. Soc.",
 fjournal={Bulletin of the Australian Mathematical Society},
 volume="72",
 year="2005",
 number="1",
 pages="147--156",
 issn="0004-9727",
 coden="ALNBAB",
 language="English",
 date="18th April, 2005",
 classmath="17B01, 17B50",
 publisher={AMPAI, Australian Mathematical Society},
 MRnumber="MR2162300",
 ZBLnumber="02212192",
 url="http://www.austms.org.au/Publ/Bulletin/V72P1/721-5118-BrKoSt/index.shtml",
 acknowledgement={},
 abstract={A theorem independently due to A.I. Shirshov and E. Witt asserts that every subalgebra of a free Lie algebra (over a field) is free. The main step in Shirshov's proof is a little known but rather remarkable result: if a set of homogeneous elements in a free Lie algebra has the property that no element of it is contained in the subalgebra generated by the other elements, then this subset is a free generating set for the subalgebra it generates. Witt also proved that every subalgebra of a free restricted Lie algebra is free. Later G.P. Kukin gave a proof of this theorem in which he adapted Shirshov's argument. The main step is similar, but it has come to light that its proof contains substantial gaps. Here we give a corrected proof of this main step in order to justify its applications elsewhere. }
}