Charles Sims (mathematician)
Encyclopedia
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....
best known for his work in 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...
. Together with Donald G. Higman
Donald G. Higman
Donald G. Higman was an American mathematician known for his discovery, in collaboration with Charles C. Sims, of the Higman–Sims group....
he discovered the Higman–Sims group, one of the sporadic group
Sporadic group
In the mathematical field of group theory, a sporadic group is one of the 26 exceptional groups in the classification of finite simple groups. A simple group is a group G that does not have any normal subgroups except for the subgroup consisting only of the identity element, and G itself...
s. The permutation group
Permutation group
In mathematics, a permutation group is a group G whose elements are permutations of a given set M, and whose group operation is the composition of permutations in G ; the relationship is often written as...
software developed by Sims also led to the proof of existence of the Lyons group
Lyons group
In the mathematical field of group theory, the Lyons group Ly , is a sporadic simple group of order...
(also known as Lyons–Sims group) and O'Nan group
O'Nan group
In the mathematical field of group theory, the O'Nan group O'N is a sporadic simple group of orderThe Schur multiplier has order 3, and its outer automorphism group has order 2...
(also known as O'Nan–Sims group).
Sims was a student of John Thompson
John G. Thompson
John Griggs Thompson is a mathematician at the University of Florida noted for his work in the field of finite groups. He was awarded the Fields Medal in 1970, the Wolf Prize in 1992 and the 2008 Abel Prize....
and received Ph.D. from Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in 1963. In his thesis he enumerated p-group
P-group
In mathematics, given a prime number p, a p-group is a periodic group in which each element has a power of p as its order: each element is of prime power order. That is, for each element g of the group, there exists a nonnegative integer n such that g to the power pn is equal to the identity element...
s, giving sharp asymptotic upper and lower bounds. Sims is one of the founders of computational group theory
Computational group theory
In mathematics, computational group theory is the study ofgroups by means of computers. It is concernedwith designing and analysing algorithms anddata structures to compute information about groups...
and is the eponym
Eponym
An eponym is the name of a person or thing, whether real or fictitious, after which a particular place, tribe, era, discovery, or other item is named or thought to be named...
of the Schreier–Sims algorithm. He was a faculty member at the Department of Mathematics at Rutgers University
Rutgers-New Brunswick
Rutgers–New Brunswick is the largest campus of Rutgers University . It is chiefly located in the City of New Brunswick and Piscataway Township...
from 1965 to 2007. During that period he had served, in particular, as Department Chair (1982–84) and Associate Provost for Computer Planning (1984–87). Sims retired from Rutgers in 2007 and currently resides in St. Petersburg
St. Petersburg, Florida
St. Petersburg is a city in Pinellas County, Florida, United States. It is known as a vacation destination for both American and foreign tourists. As of 2008, the population estimate by the U.S. Census Bureau is 245,314, making St...
, Florida.