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**Richard Neil Lyons** (born January 22, 1945 in New York City, New York)^{[1]} is an American mathematician, specializing in finite group theory.

Lyons received his PhD in 1970 at the University of Chicago under John Griggs Thompson with a thesis entitled *Characterizations of Some Finite Simple Groups with Small 2-Rank*.^{[2]} From 1972 to 2017 he was a professor at Rutgers University.

With Daniel Gorenstein and Ronald Solomon he wrote, and is continuing to write, a series on the classification program for finite simple groups, a program in which the three of them were major participants. Nine volumes of this series have been published so far. He discovered a sporadic group^{[3]} which Charles Sims constructed and called the Lyons group *Ly*.

In 2012 he shared the Leroy P. Steele Prize for Mathematical Exposition, awarded by the American Mathematical Society, with Michael Aschbacher, Stephen D. Smith, and Ronald Solomon.
In 2013 he became a fellow of the American Mathematical Society "for contributions to the classification of the finite simple groups, including the discovery of one of the 26 sporadic finite simple groups.".^{[4]}

- with Gorenstein:
*The local structure of finite groups of characteristic 2 type*, American Mathematical Society, 1983 - with Daniel Gorenstein, Ronald Solomon:
*The classification of the finite simple groups*, American Mathematical Society, 9 Vols., 1994–2021 - with Michael Aschbacher, Stephen D. Smith, Ronald Solomon:
*The classification of finite simple groups: Groups of characteristic 2 type*, American Mathematical Society, 2011

**^**"Mathematicians who classified finite simple groups". Archived from the original on September 24, 2011. Retrieved March 28, 2012.**^**Richard Lyons at the Mathematics Genealogy Project**^**Richard Lyons (1972,5) "Evidence for a new finite simple group", Journal of Algebra 20:540–569, and 34:188–189**^**List of Fellows of the American Mathematical Society

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