Burnside William
Burnside William
(b. London, England, 2 July 1852; d. West Wickham, England, 21 August 1927)
mathematics.
Burside’s research was in such diverse fields as mathematical Physics, complex function theory, geometry, group theory, and the theory of Probability. On the basis of his work in the first two field, he was elected a fellow of the Royal Society in 1893. It was to the theory of groups, however, that he made his most significant contributions. The beginnings of an interest in groups can be detected in papers of 1891 and 1892, in which groups of linear fractional transformations of a complex variable are involved. By 1894 the theory of groups of finite order had become the central concern of much of his research, and for the next twenty years Burnside remained one of the most active contributors to its development. A number of his results have become an integral part of the modern theory of groups and their representations.
With the hope of stirring up interest in group theory in England, Burnside published his Theory of Groups in 1897. It was the first treatise on groups in English and also the first to develop the theory from the modern standpoint of abstract groups vis à vis permutation groups, although this approach had already been pioneered by H. Weber in his Lehrbuch der Algebra (1896). One topic Burnside excluded from his book was that of linear groups, because it did not seem that any result could be obtained most directly by considering linear transformations. This opinion soon became outdated, however, with G. Frobenius’ development of the theory of group representations and characters (1896–1899), and Burnside was one of the first to recognize the importance of Frobenius’ ideas and to contribute to their development, simplification, and application.
Using group characters, Burnside was able to prove, for examle, that every transitive group of prime degree is either solvable or doubly transitive (1901) and that every group of order P^{a} q^{b} (p and q prime) is solvable (1904). The latter result greatly extended results of Sylow (b = 0, 1872), Frobenius (b = 1, 1895), and Jordan (b = 2, 1898). It was also Burnside who discovered that groups of odd order admit no nontrivial real irreducible representations, and he was led by its consequences to suspect that every group of odd order is solvable, W. Feit and J. G. Thompson finally established this in 1962 with a proof that involves, among other things, frequent applications of Burnside’s discovery.
Because he was convinced of the important role that representation theory was destined to play in the future advancement of group theory, Burnside devoted considerable space to its systematic presentation in the second edition of Theory of Groups (1911). This edition was widely read and is now considered a classic.
BIBLIOGRAPHY
I. Original Works, Besides Theory of Groups of Finite Order (Cambridge, 1897, 1911), Burnside also composed a treatise on probability, Theory of Probability (Cambridge, 1928), which was published posthumously.
II. Secondary Literature The only article dealing with Burnside’s life and work in any detail is A. R. Forsyth’ obituary notice in Proceedings of the Royal Society, 117A (1928), xixxv; the emphasis is upon Burnside’s early work, and insufficient attention is paid to his role in the development of the theory of groups. Some idea of the later can be obtained from the historical and survey articles scattered throughout The Collected Works of George Abram Miller, 5 vols. (Urbana, Illinois, 1935–1959), esp, II, 1–18 and III, 1–15 See also H. Burkhardt and H. Vogt, “Sur les groupes discontinus.” in Encyclopédie des sciences mathematiques, I, 1, fasc. 4 (parisLeipzig, 1909), 532–616.
Thomas Hawkins
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Burnside William." Complete Dictionary of Scientific Biography. . Encyclopedia.com. 26 Apr. 2019 <https://www.encyclopedia.com>.
"Burnside William." Complete Dictionary of Scientific Biography. . Encyclopedia.com. (April 26, 2019). https://www.encyclopedia.com/science/dictionariesthesaurusespicturesandpressreleases/burnsidewilliam
"Burnside William." Complete Dictionary of Scientific Biography. . Retrieved April 26, 2019 from Encyclopedia.com: https://www.encyclopedia.com/science/dictionariesthesaurusespicturesandpressreleases/burnsidewilliam
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.