Marshall Hall (mathematician)
Encyclopedia
Marshall Hall, Jr. was an American
mathematician
who made contributions to group theory
and combinatorics
.
, graduating in 1932. He studied further at Cambridge University, returning to Yale to take his Ph.D. in 1936 under the supervision of Øystein Ore
.
He worked in Naval Intelligence during World War II
, and in 1946 took a position at The Ohio State University. In 1959 he moved to the California Institute of Technology
and in 1985 he accepted a post at Emory University
.
Hall died in 1990 in London on his way to a conference to mark his 80th birthday.
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
s: he also worked on block designs.
His book on group theory was well received when it came out and is still useful today.
presentations of each group in the notation the text defines. "Of enduring value to those interested in finite groups" (from the preface). | lccn=6711108 }}
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who made contributions to group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
and combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
.
Career
He studied mathematics at YaleYALE
RapidMiner, formerly YALE , is an environment for machine learning, data mining, text mining, predictive analytics, and business analytics. It is used for research, education, training, rapid prototyping, application development, and industrial applications...
, graduating in 1932. He studied further at Cambridge University, returning to Yale to take his Ph.D. in 1936 under the supervision of Øystein Ore
Øystein Ore
Øystein Ore was a Norwegian mathematician.-Life:Ore was graduated from the University of Oslo in 1922, with a Cand.Scient. degree in mathematics. In 1924, the University of Oslo awarded him the Ph.D. for a thesis titled Zur Theorie der algebraischen Körper, supervised by Thoralf Skolem...
.
He worked in Naval Intelligence during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, 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 research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
and in 1985 he accepted a post at Emory University
Emory University
Emory University is a private research university in metropolitan Atlanta, located in the Druid Hills section of unincorporated DeKalb County, Georgia, United States. The university was founded as Emory College in 1836 in Oxford, Georgia by a small group of Methodists and was named in honor of...
.
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 problemBurnside'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 finitely generated 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 is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines that do not intersect...
s: he also worked on block designs.
His book on group theory was well received when it came out and is still useful today.
Publications
| lccn=595035 }}. Review by Wilhelm Magnus published in Bull. Amer. Math. Soc. Volume 66, Number 3 (1960), 144-146 and available at http://projecteuclid.org/euclid.bams/1183523505 | lccn=6416861 }}. An exhaustive catalog of the 340 groups of order dividing 64 with detailed tables of defining relations, constants, and latticeLattice of subgroups
In mathematics, the lattice of subgroups of a group G is the lattice whose elements are the subgroups of G, 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). | lccn=6711108 }}