Ferdinand Georg Frobenius

From Groupprops

This article is about a German group theorist (a German person working in group theory)

This article or section of article is sourced from:Wikipedia

Life

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

Work

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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.