Philip Hall

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Philip Hall (born April 11, 1904 in Hampstead , London , † December 30, 1982 in Cambridge ) was an English mathematician who dealt with group theory and combinatorics .

Philip Hall 1960

Life

Hall was born out of wedlock to a seamstress and attended Christ's Hospital in Horsham (after winning a scholarship) . From 1922 he studied at King's College, Cambridge University (after winning a scholarship). Reading William Burnside's book interested him in group theory. In 1925 he made his bachelor's degree and was initially undecided whether he should become a mathematician. A submitted essay on group theory ( The Isomorphisms of Abelian Groups ) earned him a fellowship from Kings College in 1927, while at the same time he worked as an assistant to the statistician Karl Pearson in London. In 1933 he became a lecturer in Cambridge. June 1939 he gave lectures in Göttingen at a group theory conference at the invitation of Helmut Hasse , which appeared in Crelle's Journal 1940. During World War II he worked in Bletchley Park as a cryptanalyst at the deciphering Italian and Japanese codes (for which he Japanese in writing and speech learned). In 1945 he was back in Cambridge, where he became a Reader in 1949 and a Sadleirian Professor in 1953 as the successor to Louis Mordell . He retired in 1967 and left Kings College in 1970.

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Hall made numerous important contributions to group theory. In 1928 he generalized the Sylow theorems of the theory of finite solvable groups (to the Hall theorems) in A note on soluble groups (Journal London Mathematical Society, 1928): Let a finite solvable group and a set of prime numbers be, then a Hall- Subgroup, and every two such Hall subgroups are conjugated. In 1934 his famous essay A contribution to the theory of groups of prime power order (Proc. London Math. Soc., Vol. 36, 1934, pp. 29-95) appeared, in which he examined regular p-groups , as well as commutator groups and Relationships with Lie rings and their identities ( Hall-Witt identities ). He presented many of his results only in lectures. He presented the Hall-Littlewood polynomials and the Hall algebra in representation theory, for example. B. in lectures at St Andrews in 1955.

He is also known for the marriage rate in combinatorics (1935).

1942 Hall was elected as a member (" Fellow ") in the Royal Society , which in 1961 awarded him the Sylvester Medal . In 1958 he received the Senior Berwick Prize of the London Mathematical Society and in 1965 their Larmor Prize and the De Morgan Medal. From 1955 to 1957 he was its President, after being its Honorary Secretary from 1938 to 1941 and 1945 to 1948.

His doctoral students include Kurt Hirsch , Bernhard Neumann , Garrett Birkhoff , James Alexander Green , Karl Gruenberg and Brian Hartley. Even Graham Higman was his student.

Fonts

literature

  • James Green, James Roseblade, John Griggs Thompson : Biographical Memoirs of Fellows of the Royal Society. Vol. 30, 1984, pp. 251-279 and Bulletin London Mathematical Society Vol. 16, 1984, pp. 603-626

Web links

Remarks

  1. ^ In addition, Hans Zassenhaus , Wilhelm Magnus , Otto Grün , Andreas Speiser , Helmut Wielandt , Ernst Witt , Wilhelm Specht gave lectures
  2. ↑ A Hall- subgroup is a subgroup of whose order is a product of prime numbers from the set of prime numbers , but whose index is not divisible by one of the prime numbers .
personal data
SURNAME Hall, Philip
BRIEF DESCRIPTION English mathematician
DATE OF BIRTH April 11, 1904
PLACE OF BIRTH Hampstead , London
DATE OF DEATH December 30, 1982
Place of death Cambridge