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Jonathan Lazare Alperin (; born 1937) is an
American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History O ...
specializing in the area of
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...
known as
group theory In 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 ...
. He is notable for his work in group theory which has been cited over 500 times according to the
Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also p ...
. The
Alperin–Brauer–Gorenstein theorem In mathematics, the Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups with quasidihedral or wreathedA 2-group is wreathed if it is a nonabelian semidirect product of a maximal subgroup that is a direct product of two cyc ...
is named after him.


Biography

Alperin attended school at
Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nin ...
and wrote his Ph.D. dissertation in 1961 "''On a Special Class of Regular p-Groups''" under the direction of
Graham Higman Graham Higman FRS (19 January 1917 – 8 April 2008) was a prominent English mathematician known for his contributions to group theory. Biography Higman was born in Louth, Lincolnshire, and attended Sutton High School, Plymouth, winning a ...
. He was awarded a
Guggenheim Fellowship Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...
in 1974. He has several times (1969, 1979, and 1983) been a visiting scholar at the
Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
. In 2012 he became a fellow of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.List of Fellows of the American Mathematical Society
retrieved 2012-11-03. Alperin was a professor at the
University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the be ...
. He has published over 60 papers and his work has been cited over 500 times. He is also known for his conjecture, , a topic of current research in
modular representation theory Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field ''K'' of positive characteristic ''p'', necessarily a prime number. As well as ha ...
, and for his work on the local control of fusion, , part of local group theory. In , the
Alperin–Brauer–Gorenstein theorem In mathematics, the Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups with quasidihedral or wreathedA 2-group is wreathed if it is a nonabelian semidirect product of a maximal subgroup that is a direct product of two cyc ...
was proven, giving the classification of
finite simple group Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked ...
s with quasi-dihedral Sylow 2-subgroups.


Selected bibliography

* * * * *


References


External links

*
Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also p ...
br>author profile
*
Home page at Chicago

Short biography
in the
Notices of the AMS ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since ...
{{DEFAULTSORT:Alperin, J. L 20th-century American mathematicians 21st-century American mathematicians Group theorists Institute for Advanced Study visiting scholars University of Chicago faculty Princeton University alumni 1937 births Living people Fellows of the American Mathematical Society