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Philip Hall FRS [1] (11 April 1904 – 30 December 1982), was an English mathematician. His major work was on group theory , notably on finite groups and solvable groups . [ 2 ] [ 3 ]
In mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and sufficient condition for an object to exist: The combinatorial formulation answers whether a finite collection of sets has a transversal —that is, whether an element can be ...
Hall algebra. For the more general Hall algebra of a category, see Ringel–Hall algebra. In mathematics, the Hall algebra is an associative algebra with a basis corresponding to isomorphism classes of finite abelian p -groups. It was first discussed by Steinitz (1901) but forgotten until it was rediscovered by Philip Hall (1959), both of whom ...
e. In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p -group G, there exists a nonnegative integer n such that the product of pn copies of g, and not fewer, is equal to the identity element.
This period saw the work of Philip Hall: on a generalization of Sylow's theorem to arbitrary sets of primes which revolutionized the study of finite soluble groups, and on the power-commutator structure of p-groups, including the ideas of regular p-groups and isoclinism of groups, which revolutionized the study of p-groups and was the first ...
Family of sets. In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection of subsets of a given set is called a family of subsets of , or a family of sets over More generally, a collection of any sets whatsoever is ...
The Sadleirian Professorship of Pure Mathematics, originally spelled in the statutes and for the first two professors as Sadlerian, [1] is a professorship in pure mathematics within the DPMMS at the University of Cambridge. It was founded on a bequest from Lady Mary Sadleir for lectureships "for the full and clear explication and teaching that ...
The commutator of two elements, g and h, of a group G, is the element. [g, h] = g−1h−1gh. This element is equal to the group's identity if and only if g and h commute (that is, if and only if gh = hg). The set of all commutators of a group is not in general closed under the group operation, but the subgroup of G generated by all commutators ...