Eamonn O'Brien | |
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 O'Brien receiving the Hector Medal in 2020 | |
| Born | Eamonn Anthony O'Brien |
| Alma mater | Australian National University |
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| Fields | Mathematician |
| Institutions | University of Auckland |
| Thesis | The Groups of Order Dividing 256 (1988) |
| Doctoral advisor | Michael F. Newman |
Eamonn Anthony O'Brien FRSNZ is a professor of mathematics at the University of Auckland, New Zealand, known for his work in computational group theory and p-groups.
O'Brien obtained his B.Sc. (Hons) from the National University of Ireland (Galway) in 1983. He completed his Ph.D. in 1988 at the Australian National University. His dissertation, The Groups of Order Dividing 256, was supervised by Michael F. Newman. [1]
O'Brien's early work concerned classification, up to isomorphism, of groups of order 256. [2] He developed early computer software to complete the classification, and to verify that the classification can correct errors in earlier counting. This led to classifications of many further families of small order groups. In 2000, together with Bettina Eick and Hans Ulrich Besche, O'Brien classified all groups of order at most 2000, excluding those of order 1024. The groups of order 1024 were instead enumerated. [3] This classification is known as the Small Groups Library. Later with Michael F. Newman and Michael Vaughan-Lee O'Brien extended the classifications of groups of order , , and . These classifications comprise the tables provided in the computer algebra systems SageMath, GAP, and Magma.
For a 20-year span from the mid-1990s, O'Brien led the so-called Matrix Group Recognition Project whose primary objective is to solve the following problem: given a list of invertible matrices over a finite field, determine the composition series of the group. [4] [5] Implementations of algorithms that realize the goals of this project form the bedrock of matrix group computations in the computer algebra system Magma.
O'Brien's collaborations include resolution of several conjectures include the Ore conjecture, according to which all elements of non-abelian finite simple groups are commutators. [6]
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. The orders of different elements may be different powers of p.
In abstract algebra an inner automorphism is an automorphism of a group, ring, or algebra given by the conjugation action of a fixed element, called the conjugating element. They can be realized via simple operations from within the group itself, hence the adjective "inner". These inner automorphisms form a subgroup of the automorphism group, and the quotient of the automorphism group by this subgroup is defined as the outer automorphism group.
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Aner Shalev is a professor at the Einstein Institute of Mathematics at the Hebrew University of Jerusalem, and a writer.
In mathematical finite group theory, the L-balance theorem was proved by Gorenstein & Walter (1975). The letter L stands for the layer of a group, and "balance" refers to the property discussed below.
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In computational group theory, a black box group is a group G whose elements are encoded by bit strings of length N, and group operations are performed by an oracle. These operations include:
Pham Huu Tiep is a Vietnamese American mathematician specializing in group theory and representation theory. He is currently a Joshua Barlaz Distinguished Professor of Mathematics at Rutgers University.
Bettina Eick is a German mathematician specializing in computational group theory. She is Professor of Mathematics at the Technische Universität (TU) Braunschweig.
Martin Liebeck is a professor of Pure Mathematics at Imperial College London whose research interests include group theory and algebraic combinatorics.
Wallace Smith Martindale III is an American mathematician, known for Martindale's Theorem (1969) and the Martindale ring of quotients introduced in the proof of the theorem. His 1969 paper generalizes Posner's theorem and a theorem of Amitsur and gives an independent, unified proof of the two theorems.
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