Michael Ernest O'Nan (August 9, 1943,

Fort Knox, Kentucky Fort Knox is a United States Army installation in Kentucky, south of Louisville and north of Elizabethtown, Kentucky, Elizabethtown. It is adjacent to the United States Bullion Depository (also known as Fort Knox), which is used to house a larg ...

– July 31, 2017,

Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri ...

) was an American mathematician, specializing in group theory. O'Nan received his PhD in 1970 from

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

under

Daniel Gorenstein Daniel E. Gorenstein (January 1, 1923 – August 26, 1992) was an American mathematician best remembered for his contribution to the classification of finite simple groups. Gorenstein mastered calculus at age 12 and subsequently matriculated at ...

with thesis ''A Characterization of the Three-Dimensional Projective Unitary Group over a Finite Field''. He was a professor at

Rutgers University Rutgers University ( ), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of three campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's C ...

. In 1976 he found strong evidence for the existence of a

sporadic group In the mathematical classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic finite groups, or just the sporadic groups. A simpl ...

, which Charles Sims constructed. The group is commonly called the

O'Nan group In the area of abstract algebra known as group theory, the O'Nan group ''O'N'' or O'Nan–Sims group is a sporadic simple group of order : 460,815,505,920 = 2934573111931 ≈ 5. History ''O'N'' is one of the 26 sporadic group ...

after O'Nan. The

O'Nan–Scott theorem In mathematics, the O'Nan–Scott theorem is one of the most influential theorems of permutation group theory; the classification of finite simple groups is what makes it so useful. Originally the theorem was about maximal subgroups of the symmet ...

in group theory is also named after O'Nan, who discovered it independently from Leonard Scott. It describes the

maximal subgroup In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra. In group theory, a maximal subgroup ''H'' of a group ''G'' is a proper subgroup, such that no proper subgroup ''K'' contains ''H'' ...

s of the

symmetric group In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric grou ...

Selected works

* ''Linear Algebra'' (= ''Eagle Mathematics Series.'' vol. 2A). Harcourt Brace Jovanovich, New York NY, 1971, (2nd edition.1976, ; 3rd edition. with Herbert Enderton. Harcourt Brace Jovanovich, San Diego CA, 1990, ). * *

References

1943 births 2017 deaths 20th-century American mathematicians Group theorists Princeton University alumni Rutgers University faculty 21st-century American mathematicians People from Hardin County, Kentucky {{US-mathematician-stub