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Marshall Hall (mathematician)

 

 
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Marshall Hall (mathematician)
 
 
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Marshall Hall, Jr. (17 September 1910, St Louis, Missouri – 4 July 1990, London
London

London is the capital of both England and the United Kingdom, and the most populous municipality in the European Union. An important settlement for two millennia, History of London goes back to its founding by the Roman Empire....
) was an American
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
 mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
 who made contributions to group theory
Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as group .The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring , field , and vector spaces can all be seen as groups endowed with additional operations and axioms....
 and combinatorics
Combinatorics

Combinatorics is a branch of pure mathematics concerning the study of Countable set objects. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects in computer science and statistical physics....
.

He studied mathematics at Yale
YALE

RapidMiner is an environment for machine learning and data mining experiments. It allows experiments to be made up of a large number of arbitrarily nestable operators, described in XML files which can easily be created with RapidMiner's graphical user interface....
, graduating in 1932. He studied further at Cambridge University, returning to Yale to take his Ph.D. in 1936 under the supervision of Oystein Ore.

He worked in Naval Intelligence during World War II
World War II

World War II, or the Second World War , was a global military conflict which involved a Participants in World War II, including all of the great powers, organised into two opposing military alliances: the Allies of World War II and the Axis powers....
, and in 1946 took a position at The Ohio State University.






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Marshall Hall, Jr. (17 September 1910, St Louis, Missouri – 4 July 1990, London
London

London is the capital of both England and the United Kingdom, and the most populous municipality in the European Union. An important settlement for two millennia, History of London goes back to its founding by the Roman Empire....
) was an American
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
 mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
 who made contributions to group theory
Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as group .The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring , field , and vector spaces can all be seen as groups endowed with additional operations and axioms....
 and combinatorics
Combinatorics

Combinatorics is a branch of pure mathematics concerning the study of Countable set objects. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects in computer science and statistical physics....
.

He studied mathematics at Yale
YALE

RapidMiner is an environment for machine learning and data mining experiments. It allows experiments to be made up of a large number of arbitrarily nestable operators, described in XML files which can easily be created with RapidMiner's graphical user interface....
, graduating in 1932. He studied further at Cambridge University, returning to Yale to take his Ph.D. in 1936 under the supervision of Oystein Ore.

He worked in Naval Intelligence during World War II
World War II

World War II, or the Second World War , was a global military conflict which involved a Participants in World War II, including all of the great powers, organised into two opposing military alliances: the Allies of World War II and the Axis powers....
, and in 1946 took a position at The Ohio State University. In 1959 he moved to the California Institute of Technology
California Institute of Technology

The California Institute of Technology is a private university research university located in Pasadena, California, United States. Caltech maintains a strong emphasis on the natural sciences and engineering....
 and in 1985 he accepted a post at Emory University
Emory University

Emory University is a private university located in the metropolitan area of the city of Atlanta, Georgia in western unincorporated area DeKalb County, Georgia, Georgia , United States....
.

Hall died in 1990 in London on his way to a conference to mark his 80th birthday.

He wrote a number of papers of fundamental importance in group theory, including his solution of Burnside's problem
Burnside's problem

The Burnside problem, posed by William Burnside in 1902 and one of the oldest and most influential questions in group theory, asks whether a generating set of a group group in which every element has finite Order must necessarily be a finite group....
 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 plane
Projective plane

In mathematics, a projective plane has two possible definitions, one of them coming from linear algebra, and another coming from axiomatic geometry and finite geometry....
s: he also worked on block designs.

Publications

, }} , }}. An exhaustive catalog of the 340 groups of order dividing 64 with detailed tables of defining relations, constants, and lattice
Lattice of subgroups

In mathematics, the lattice of subgroups of a Group is the Lattice whose elements are the subgroups of , with the partial order Relation being set inclusion....
 presentations of each group in the notation the text defines. "Of enduring value to those interested in finite groups" (from the preface). , }}

External links