:''This English mathematician is sometimes confused with the Irish mathematician
William S. Burnside (1839–1920).''
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William Burnside (2 July 1852 – 21 August 1927) was an English
mathematician. He is known mostly as an early researcher in the theory of
finite groups.
Burnside was born in
London in 1852. He went to school at
Christ's Hospital
Christ's Hospital is a Public school (United Kingdom), public school (English Independent school (United Kingdom), independent boarding school for pupils aged 11–18) with a royal charter located to the south of Horsham in West Sussex. The scho ...
until 1871 and attended
St. John's and
Pembroke Colleges at the
University of Cambridge, where he was the
Second Wrangler
At the University of Cambridge in England, a "Wrangler" is a student who gains first-class honours in the final year of the university's degree in mathematics. The highest-scoring student is the Senior Wrangler, the second highest is the Se ...
(bracketed with
George Chrystal) in 1875. He lectured at Cambridge for the following ten years, before being appointed professor of mathematics at the
Royal Naval College in
Greenwich. While this was a little outside the main centres of British mathematical research, Burnside remained a very active researcher, publishing more than 150 papers in his career.
Burnside's early research was in
applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical ...
. This work was of sufficient distinction to merit his election as a fellow of the
Royal Society in 1893, though it is little remembered today. Around the same time as his election his interests turned to the study of
finite groups. This was not a widely studied subject in
Britain
Britain most often refers to:
* The United Kingdom, a sovereign state in Europe comprising the island of Great Britain, the north-eastern part of the island of Ireland and many smaller islands
* Great Britain, the largest island in the United King ...
in the late 19th century, and it took some years for his research in this area to gain widespread recognition.
The central part of Burnside's group theory work was in the area of
group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to ...
s, where he helped to develop some of the foundational theory, complementing, and sometimes competing with, the work of
Ferdinand Georg Frobenius, who began his research in the subject during the 1890s. One of Burnside's best known contributions to group theory is his
''paqb'' theorem, which shows that every finite group whose order is divisible by fewer than three distinct primes is
solvable.
In 1897 Burnside's classic work ''Theory of Groups of Finite Order'' was published.
[ The second edition (pub. 1911) was for many decades the standard work in the field. A major difference between the editions was the inclusion of ]character theory
In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information abo ...
in the second.
Burnside is also remembered for the formulation of Burnside's problem that concerns the question of bounding the size of a group if there are fixed bounds both on the order of all of its elements and the number of elements needed to generate it, and also for Burnside's lemma (a formula relating the number of orbits of a permutation group acting on a set with the number of fixed points of each of its elements) though the latter had been discovered earlier and independently by Frobenius and Augustin Cauchy
Baron Augustin-Louis Cauchy (, ; ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He w ...
.
He received an honorary doctorate (D.Sc.
Doctor of Science ( la, links=no, Scientiae Doctor), usually abbreviated Sc.D., D.Sc., S.D., or D.S., is an academic research degree awarded in a number of countries throughout the world. In some countries, "Doctor of Science" is the degree used f ...
) from the University of Dublin in June 1901.
In addition to his mathematical work, Burnside was a noted rower. While he was a lecturer at Cambridge, he also coached the rowing crew team. In fact, his obituary in '' The Times'' took more interest in his athletic career, calling him "one of the best known Cambridge athletes of his day".
He is buried at the West Wickham Parish Church in South London.
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{{DEFAULTSORT:Burnside, William
1852 births
1927 deaths
19th-century English mathematicians
20th-century English mathematicians
Group theorists
People educated at Christ's Hospital
Alumni of St John's College, Cambridge
Alumni of Pembroke College, Cambridge
Academics of the Royal Naval College, Greenwich
Royal Medal winners
Second Wranglers
Fellows of the Royal Society
De Morgan Medallists