Philip Hall

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

Life

Hall was born as an illegitimate child of a seamstress and attended ( after he won a scholarship ) the Christ's Hospital in Horsham. From 1922 he studied at King 's College, Cambridge University ( after he had won a scholarship ). The reading of William Burnside's book interested him for the group theory. In 1925, he earned his bachelor 's degree and was initially undecided whether he should be a mathematician. However, a submitted essay on Group Theory (The Isomorphisms of Abelian Groups) gave him in 1927 a Fellowship of King's College, while he worked simultaneously as an assistant for the statistician Karl Pearson in London. In 1933 he was a lecturer at Cambridge. June 1939 he lectured in Göttingen on a group theory conference at the invitation of Helmut Hasse, who appeared in Crelle 's Journal 1940. During the Second World War he worked at Bletchley Park as a cryptographer to decipher Italian and Japanese codes (for which he learned Japanese in writing and speech ). In 1945 he was back in Cambridge, where in 1953 he became Reader in 1949 and as the successor of Louis Mordell Sadleirian professor. In 1967, he retired in 1970 and left the Kings College.

Work

Hall made ​​many important contributions to group theory. In 1928, he generalized the Sylow - sets of the theory of finite solvable groups ( the Hall - sets ) in A note on soluble groups (Journal London Mathematical Society, 1928): Let be a finite solvable group and a set of primes, then has a Hall sub- group and two such Hall - subgroups are conjugated. In 1934 he published his famous essay A contribution to the theory of groups of prime power order ( Proc. London Math Soc., Vol 36, 1934, pp. 29-95 ) in which he examined regular p-groups, as well as Kommutatorgruppen and relationships with Lie rings and their identities ( Hall -Witt identity ). Many of his results he presented only in lectures. The Hall - Littlewood polynomials and the Hall algebra in representation theory he presented eg in lectures before in St Andrews in 1955.

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

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

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

Writings

• Collected Works. Oxford, Clarendon Press 1988.
• Papers in the Journal of Pure and Applied Mathematics ( " Crelle 's Journal " ) Bd.182, 1940 ( Group Theory Conference in June 1939, Göttingen ): Table of contents with the lecture titles
• Hall: Verbal and marginal subgroups.
• Hall: The classification of prime -power groups.
• Hall: On groups of automorphisms.
• Hall: The construction of soluble groups.