Presentations for Certain Chevalley Groups

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Let G = P SLn(K), n ≥ 3, K a division ring or Dn(K), n ≥ 4 or En(K), 6 ≤ n ≤ 8, K a field. Then two types of presentations for G are given. In the first, G is generated by SL2(K)'s which satisfies relations according to the Dynkin diagram of G. In the second, G is generated by a set {Ai | i ∈ I} of Abelian groups, which satisfy relations similar to the root subgroups of G.

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