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This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.
This open access book presents a comprehensive synthesis of the biodiversity of the oceanic islands of the Gulf of Guinea, a biodiversity hotspot off the west coast of Central Africa. Written by experts, the book compiles data from a plethora of sources – archives, museums, bibliography, official reports and previously unpublished data – to provide readers with the most updated information about the biological richness of these islands and the conservation issues they face. The Gulf of Guinea Oceanic Islands (Príncipe, São Tomé and Annobón and surrounding islets) present extraordinary levels of endemism across different animal, fungi and plant groups. This very high endemism likely r...
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