## A generalization of a theorem of J. Nielsen concerning hyperbolic groups |

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abelian group According to proposition adjoint group automorphism with simple canonical decomposition canonical neighbourhood Cartan central subgroup centre closure commutatieve complementary normal divisor completely reducible complex extension complex infinitesimal group consequently contains a normal coset denote direct product direct sum discrete group divisor of finite divisors and real elements a satisfying endomorphism exponential mapping finite index Further homeomorphic HYPERBOLIC GROUPS hyperbolic plane identiteit induces infinitesimal automorphism infinitesimal element inner product invariant subspaces invariant with respect irreducible with respect isometric transformations isomorphic Lemma Lie subgroup Liese groep linear group linear mapping locally hyperbolic subgroup mapping which commutes Nielsen Proof prove rationally closed real automorphisms real characteristic roots real linear subspace real semi real semi-simple group real subgroup representation represented as exp satisfying x,x semi-simple normal divisor simple elementary divisors simple group simple Lie groups soluble normal divisor stelling theorems transvections vector wordt zijn