Representations of Finite Groups and Algebras

Abstract

The theory of representations of finite groups by matrices with complex matrix elements was developed, nearly simultaneously, by three authors: Theodor Molien, Georg Frobenius, and William Burnside. Their earliest papers on this subject are:

• Th. Molien: Eine Bemerkung zur Theorie der homogenen Substitutionsgruppen, Sitzungsberichte der Naturforscher-Gesellschaft Dorpat (= Yurev in Estonia) 11, p. 259–276, presented April 24, 1897,

• Th. Molien: Über die Anzahl der Variablen einer irreduziblen Substitutionsgruppe, same volume, p. 277–288, presented September 25, 1897,

• G. Frobenius: Über die Darstellung der endlichen Gruppen durch lineare Transformationen, Sitzungsber. preuss. Akad. Berlin 1897, presented November 18, 1897,

• W. Burnside: On the Continuous Group that is Defined by Any Given Group of Finite Order, Proceedings London Math. Soc. 29, p. 207–225, read January 10, 1898,

• W. Burnside: Same title (second paper), same volume, p. 546–565, read June 9, 1898.