Talk:Complemented group

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Distinct definitions[edit]

There are two definitions of complemented group; the original by Hall requires group theoretic complements, but a later definition by Zacher only requires lattice theoretic complements. The first was taken up by Černikov and the Russian school and remains an active area of research today. The second is concentrated in the Italian school, but is covered quite well in Schmidt's Lattices book with a nice bibliography. The alternating group of degree four is Zacher complemented but not Hall-Černikov complemented. Both meanings appear notable, and are very similar at first glance, so it might be best to keep them in the same article. JackSchmidt (talk) 03:44, 31 March 2010 (UTC)