Gersten's theorem
If φ is an automorphism of a finitely generated free group F then { x : x ∈ F and φ(x) x} is finitely generated. [6] [7]
Stephen M. Gersten (born 2 December 1940) is an American mathematician, specializing in finitely presented groups and their geometric properties. [1]
Gersten graduated in 1961 with an AB from Princeton University [1] and in 1965 with a PhD from Trinity College, Cambridge. His doctoral thesis was Class Groups of Supplemented Algebras written under the supervision of John R. Stallings. [2] In the late 1960s and early 1970s he taught at Rice University. In 1972–1973 he was a visiting scholar at the Institute for Advanced Study. [3] In 1973 he became a professor at the University of Illinois at Urbana–Champaign. [1] In 1974 he was an Invited Speaker at the International Congress of Mathematicians in Vancouver. [4] At the University of Utah he became a professor in 1975 and is now semi-retired there. [1] His PhD students include Roger C. Alperin, R. Keith Dennis and Edward W. Formanek. [2]
Gersten's conjecture has motivated considerable research. [5]
If φ is an automorphism of a finitely generated free group F then { x : x ∈ F and φ(x) x} is finitely generated. [6] [7]
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