Ferdinand Georg Frobenius

Personal life
Ferdinand Georg Frobenius (October 26, 1849 Charlottenburg, Berlin - August 3, 1917) was a German mathematician who worked in group theory and the theory of differential equations.

Professional life

 * Schooling (till 1870): University of Berlin
 * 1870-? : Taught in Berlin
 * Received an appointment at the Polytechnicium in Zurich
 * 1893: Was elected to the Prussian Academy of Science at Berlin

Proof of Sylow's theorems
Frobenius was the first person to prove Sylow's theorem in the context of abstract groups (earlier proofs had been in the context of permutation groups). His proof is still the one used in group theory texts.

Frobenius groups
Frobenius studied a particular kind of group action giving rise to the notion of Frobenius group, Frobenius complement and Frobenius kernel.

Frobenius reciprocity
This foundational result in group representations, that relates induced representations and restrictions, was discovered by Frobenius while studying the theory of linear representations.

Terms

 * Frobenius group
 * Frobenius kernel
 * Frobenius complement

Results

 * Frobenius reciprocity

Collaborators

 * Ludwig Sylow

Competitors

 * William Burnside

Advisors

 * Karl Weierstrass
 * Ernst Kummer

Students

 * Richard Fuchs