| Crynodeb: | <p>The last fifteen years of the nineteenth century saw great changes in the perception
and formulation of group theory and Galois theory. At that time, the major problems
which became the focus of twentieth-century finite group theory were distilled. New
techniques and systematic methods were introduced as attempts were made to solve
these problems. The abstraction of group theory which had taken place during the
1870s and 1880s resulted in deeper insights into Galois' theory of equations.</p>
<p>This thesis focuses on the algebraic studies of the German mathematician Otto Holder
(1859-1937). It consists largely of a historical and critical analysis of his original work
on group theory and Galois theory, which was published in seven articles between 1889
and 1895. Holder was instrumental in providing a clear understanding of the structure
which a theory of finite groups should possess. The important mathematical problems
that arise from such an understanding are formulated in his papers. He developed
techniques and methods of solution which had a great influence on the direction of
subsequent research on these problems.</p>
<p>A biography of Otto Holder is presented in Chapter 2 of the thesis; a survey of the
algebraic inheritance on which he drew forms the substance of Chapter 3. The following
six chapters each examine his contribution to a specific area or problem and discuss
the context of his work. His mathematics is related to and contrasted with modern
techniques and methods of solution, which are included where appropriate. Each chapter
concludes with some remarks on the later development of the ideas and problems Holder
considered. The subjects of these chapters are successively the re-formulation of Galois
theory, the concept of quotient group, the Jordan—Holder Theorem for finite groups,
the search for simple groups, the structure theory of finite groups and group extension
theory. Finally, various conclusions are drawn about Otto Holder's achievements and
his place in the history of algebra.</p>
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