Marshall Hall Jr. (17 September 1910 – 4 July 1990) was an American mathematician who made significant contributions to group theory and

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

Career

Hall studied mathematics at Yale University, graduating in 1932. He studied for a year at Cambridge University under a Henry Fellowship working with G. H. Hardy. He returned to Yale to take his Ph.D. in 1936 under the supervision of

Øystein Ore Øystein Ore (7 October 1899 – 13 August 1968) was a Norwegian mathematician known for his work in ring theory, Galois connections, graph theory, and the history of mathematics. Life Ore graduated from the University of Oslo in 1922, with a ...

. He worked in Naval Intelligence during World War II, including six months in 1944 at Bletchley Park, the center of British wartime code breaking. In 1946 he took a position at Ohio State University. In 1959 he moved to the California Institute of Technology where, in 1973, he was named the first IBM Professor at Caltech, the first named chair in mathematics. After retiring from Caltech in 1981, he accepted a post at Emory University in 1985. Hall died in 1990 in London on his way to a conference to mark his 80th birthday.

Contributions

He wrote a number of papers of fundamental importance in group theory, including his solution of Burnside's problem for groups of exponent 6, showing that a finitely generated group in which the order of every element divides 6 must be finite. His work in combinatorics includes an important paper of 1943 on projective planes, which for many years was one of the most cited mathematics research papers.Mathematics Department of Ohio State Universitybr>Marshall Hall Jr.
via Wayback Machine In this paper he constructed a family of non-Desarguesian planes which are known today as

Hall plane In mathematics, a Hall plane is a non-Desarguesian projective plane constructed by Marshall Hall Jr. (1943). There are examples of order ''p''2''n'' for every prime ''p'' and every positive integer ''n'' provided ''p''2''n'' > 4. Algebraic con ...

s. He also worked on

block design In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as ''blocks'', chosen such that frequency of the elements satisfies certain conditions making the collection of bl ...

s and coding theory. His classic book on group theory was well received when it came out and is still useful today. His book ''Combinatorial Theory'' came out in a second edition in 1986, published by John Wiley & Sons. He proposed

Hall's conjecture In mathematics, Hall's conjecture is an open question, , on the differences between perfect squares and perfect cubes. It asserts that a perfect square ''y''2 and a perfect cube ''x''3 that are not equal must lie a substantial distance apart. This q ...

on the differences between

perfect squares In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The u ...

and

perfect cubes In arithmetic and algebra, the cube of a number is its third power, that is, the result of multiplying three instances of together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example or . T ...

, which remains an open problem as of 2015.

Publications

* 1943: "Projective Planes", Transactions of the American Mathematical Society 54(2): 229–77 * 1959: ''The Theory of Groups'', Macmillan ** Wilhelm Magnus (1960
Review: Marshall Hall, Jr. ''Theory of Groups''
Bulletin of the American Mathematical Society 66(3): 144–6. * 1964: (with James K. Senior) ''The Groups of Order 2ⁿ n ≤ 6)'',

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** Preface: "An exhaustive catalog of the 340 groups of order dividing 64 with detailed tables of defining relations, constants, and lattice presentations of each group in the notation the text defines. "Of enduring value to those interested in finite groups". * 1967: ''Combinatorial Theory'',

Blaisdell Blaisdell is a surname. Notable people with the surname include: *Alfred Blaisdell, politician from North Dakota *Daniel Blaisdell, politician from New Hampshire *Frances Blaisdell, musician from New Jersey *Frank Ellsworth Blaisdell (1862–1946), ...

Notes

References

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External links

* * {{DEFAULTSORT:Hall, Marshall Jr 1910 births 1990 deaths 20th-century American mathematicians Mathematicians from Missouri Scientists from St. Louis Algebraists Group theorists Emory University faculty Combinatorialists California Institute of Technology faculty Ohio State University faculty Yale Graduate School of Arts and Sciences alumni Yale College alumni