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I would like to thank Prof. Dr. Torsten Braun, head of the Computer Network and Distributed Systems group (RVS), for supervising this work and for his insightful advises. Prof. Dr. Torsten Braun encouraged and motivated me to publish my research results and he provided me the opportunity to present

the residual finiteness of outer automorphisms of relatively hyperbolic groups

2010 to my wife, Joyce, and my family...- Résumé-

the group elements are data structures in a computer. Matrices are unnecessarily large structures, and part of this thesis is concerned with small and efficient representations of a large class of Coxeter groups (including most Coxeter groups that anyone ever payed any attention to.) The main contents

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are client-server based, which is feasible for relatively slow role-playing games. Those have modest bandwidth and latency requirements and are paid for by their customers. For MMOGs with higher realtime requirements and/or a smaller number of customers willing to pay, peer-to-peer networking seems to be a

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