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  • STRUCTURE AND PRESENTATIONS OF LIE-TYPE GROUPS

  • F. G. TIMMESFELD
  • Journal:
    Proceedings of the London Mathematical Society / Volume 81 / Issue 2 / September 2000
    Published online by Cambridge University Press:
    19 October 2000, pp. 428-484
    Print publication:
    September 2000

  • Let $\mathcal{B}$ be an irreducible spherical Moufang building of rank at least $2$. Thenthe group $G$ is called a group of Lie type$\mathcal{B}$ if it is generated by theroot subgroups corresponding to the rootsof some apartments of $\mathcal{B}$. This notion includes:\begin{enumerate}\item[(1)] classical groups of finite rank,\item[(2)] simple algebraic groups over arbitrary fields,\item[(3)] the `mixed' groups of Tits.\end{enumerate} General structure theorems and a general presentation type theorem for such Lie-type groups, which in a way generalize well-knowntheorems of Seitz and Curtis and Tits, are obtained. 1991 Mathematics Subject Classification:20G15, 20E42.