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Hall was the main impetus behind the British school of group theory and the growth of group theory to be one of the major mathematical topics of the 20 C was largely due to him.
Hall went up to King's College Cambridge in 1922. Hall's interest in group theory came from Burnside's book. He offered parts of that book for examination in the Tripos. He graduated in 1925.
Hall worked as a research assistant of Karl Pearson and his first published papers are in the theory of correlation. Returning to Cambridge in 1927 to take up a Fellowship at King's he made an important discovery in group theory, generalising the Sylow thoerems for finite soluble groups to prove what are now called Hall's theorems.
In 1932 Hall wrote what is perhaps his most famous paper A contribution to the theory of groups of prime power order . It is a beautiful paper which is one of the fundamental sources of modern group theory.
During the war he made an important contribution with his work at the Code and Cypher School at Bletchley Park.
In 1957 Hall gave a series of lectures on nilpotent groups which have had great influence ever since.
His work on infinite groups comes in papers of 1952, 1959 and 1961. The ideas of these papers continue to be one of the main areas of group theory research.
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