William Burnside

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William Burnside

William Burnside (born July 2, 1852 in the Paddington district of London ; † August 21, 1927 in Cotleigh in West Wickham , Kent ) was an English mathematician who is best known for his contributions to group theory .

life and work

Burnside was the son of a Scottish merchant; However, he was orphaned at the age of six and was brought up at a school for the children of poor people (Christ's Hospital). After winning a scholarship, he entered St. John's College in Cambridge in 1871 , but moved (to have better chances in the rowing team) to Pembroke College , where he emerged as Second Wrangler in the Tripos in 1875 . He also won the Smith Prize and became a Fellow of the Pembroke. Burnside (who, in addition to Arthur Cayley , had heard from the astronomer John Couch Adams and the physicists George Gabriel Stokes and James Clerk Maxwell ), was initially interested in hydrodynamics , to which he applied methods of function theory. In 1885 he became a professor at the Royal Naval College in Greenwich . There he stayed, despite Cambridge University's offer to take over the chair from Stokes. In 1886 he married a Scot. The marriage resulted in two sons and three daughters.

Burnside is best known for his work on group theory (the theory of finite groups), which he turned to from 1893. In 1897 he published his main work Theory of groups of finite order . It is the first English textbook on the subject that was not very popular among English mathematicians at the time. In 1899 he received the de Morgan Medal of the London Mathematical Society for this achievement. His best-known result is the theorem that groups of the order (p, q prim) are solvable (special cases have already been proven by Peter Ludwig Mejdell Sylow , Ferdinand Georg Frobenius and Camille Jordan ). His conjecture that all finite groups of odd order are resolvable was only proven in the 1960s by Walter Feit and John Griggs Thompson in a major mathematical tour de force . The Burnside problem is still a driving force in group theory today : it asks whether all finitely generated groups, whose elements g all have a finite order (i.e. there is a natural number n with , the group is periodic ), are finite . Burnside explains in the second edition of his group theory book the theory of group characters by Frobenius.

Burnside finally turned to probability theory and wrote a book about it that appeared posthumously in 1928.

He is not to be confused with William Snow Burnside (1839–1920) from Dublin, author of Theory of Equations .

Honors

In 1893 he was made a member ("Fellow") of the Royal Society , which in 1904 awarded him the Royal Medal "for his research in mathematics, especially in group theory".

See also

Web links

Remarks

  1. ↑ It was answered negatively in particular by the work of Russian mathematicians such as Igor Schafarewitsch and Pjotr ​​Sergejewitsch Novikow . Efim Zelmanov received the Fields Medal in 1994 for the affirmative solution to the limited Burnside problem
  2. ^ Peter Neumann in Burnside Collected Works , Oxford University Press 2004, Volume 1, p. 16
personal data
SURNAME Burnside, William
ALTERNATIVE NAMES Burnside, William Snow (full name)
BRIEF DESCRIPTION English mathematician
DATE OF BIRTH July 2, 1852
PLACE OF BIRTH London
DATE OF DEATH August 21, 1927
Place of death Cotleigh , Kent