Philip Hall
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Philip Hall FRS (11 April 1904 – 30 December 1982), was an English
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
. His major work was on
group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
, notably on
finite group Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked ...
s and
solvable group In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates ...
s.


Biography

He was educated first at
Christ's Hospital Christ's Hospital is a public school (English independent boarding school for pupils aged 11–18) with a royal charter located to the south of Horsham in West Sussex. The school was founded in 1552 and received its first royal charter in 1553 ...
, where he won the Thompson Gold Medal for mathematics, and later at
King's College, Cambridge King's College is a constituent college of the University of Cambridge. Formally The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies beside the River Cam and faces out onto King's Parade in the centre of the city ...
. He was elected a
Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
in 1951 and awarded its
Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry a ...
in 1961. He was President of the
London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...
in 1955–1957, and awarded its
Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the ...
in 1958 and
De Morgan Medal The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the societ ...
in 1965.


Publications

* * *


See also

* Abstract clone *
Commutator collecting process In group theory, a branch of mathematics, the commutator collecting process is a method for writing an element of a group as a product of generators and their higher commutators arranged in a certain order. The commutator collecting process was int ...
*
Isoclinism of groups In mathematics, specifically group theory, isoclinism is an equivalence relation on groups which generalizes isomorphism. Isoclinism was introduced by to help classify and understand p-groups, although it is applicable to all groups. Isoclinism al ...
*
Regular p-group In mathematical finite group theory, the concept of regular ''p''-group captures some of the more important properties of abelian ''p''-groups, but is general enough to include most "small" ''p''-groups. Regular ''p''-groups were introduced by . ...
*
Three subgroups lemma In mathematics, more specifically group theory, the three subgroups lemma is a result concerning commutators. It is a consequence of Philip Hall and Ernst Witt's eponymous identity. Notation In what follows, the following notation will be employed ...
* Hall algebra, and Hall polynomials *
Hall subgroup In mathematics, specifically group theory, a Hall subgroup of a finite group ''G'' is a subgroup whose order is coprime to its index. They were introduced by the group theorist . Definitions A Hall divisor (also called a unitary divisor) of a ...
*
Hall–Higman theorem In mathematics, mathematical group theory, the Hall–Higman theorem, due to , describes the possibilities for the minimal polynomial (linear algebra), minimal polynomial of an element of prime power order for a representation of a p-solvable gr ...
* Hall–Littlewood polynomial * Hall's universal group *
Hall's marriage theorem In mathematics, Hall's marriage theorem, proved by , is a theorem with two equivalent formulations: * The combinatorial formulation deals with a collection of finite sets. It gives a necessary and sufficient condition for being able to select a di ...
*
Hall word In mathematics, in the areas of group theory and combinatorics, Hall words provide a unique monoid factorisation of the free monoid. They are also totally ordered, and thus provide a total order on the monoid. This is analogous to the better-known ...
* Hall–Witt identity *
Irwin–Hall distribution In probability and statistics, the Irwin–Hall distribution, named after Joseph Oscar Irwin and Philip Hall, is a probability distribution for a random variable defined as the sum of a number of independent random variables, each having a unifo ...
*
Zappa–Szép product In mathematics, especially group theory, the Zappa–Szép product (also known as the Zappa–Rédei–Szép product, general product, knit product, exact factorization or bicrossed product) describes a way in which a group can be constructed fro ...


References

1904 births 1982 deaths 20th-century English mathematicians Algebraists Group theorists People educated at Christ's Hospital Alumni of King's College, Cambridge Fellows of the Royal Society Bletchley Park people Presidents of the London Mathematical Society Sadleirian Professors of Pure Mathematics {{UK-mathematician-stub