Group-Characters of Various Linear Groups

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Excerpt from Group-Characters of Various Linear Groups: A Dissertation Submitted to the Faculty of the Ogden Graduate School of Science, in Candidacy for the Degree of Doctor of Philosophy, Department of MathematicsIn Part I we consider the group HE sle (2, p 2, of all binary linear homogeneous substitutions in the GF [pn], of determinant unity. By the aid of two theorems due to Frobenius on the relation between the characters of a group and those Of one of its quotient-groups, we deduce as a corollary the char actera of the group FE lf(2, p 2, of all binary linear fractional subeti tutions in the GF [p] of determinant unity (when in their normal forms). We have also obtained these characters directly by the method applied to the group H the chief points of difference in the treatment are stated in foot-notes. The results are a direct generalization of those Obtained by Frobenius. In Part II we consider the group 1715 sle (2, p: 2. This is identical with the group LF (2, p 2. Part III deals with the group F, of all binary linear fractional substitutions in the p>2, of determinant not zero. The group H is treated with considerable detail, the others brie¿y.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.