Ludwig Georg Elias Moses Bieberbach (German: [ˈbiːbɐˌbaχ]; 4 December 1886 – 1 September 1982) was a German mathematician.
== Biography ==
Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorate in 1910. His dissertation was titled On the theory of automorphic functions (German: Theorie der automorphen Funktionen). He began working as a Privatdozent at Königsberg in 1910 and as Professor ordinarius at the University of Basel in 1913. He taught at the University of Frankfurt in 1915 and the University of Berlin from 1921–45.
Bieberbach...
In the area of modern algebra known as group theory, the Tits group 2F4(2)′, named for Jacques Tits (French: [tits]), is a finite simple group of order
211 · 33 · 52 · 13 = 17971200
≈ 2×107.
It is sometimes considered a 27th sporadic group.
== History and properties ==
The Ree groups 2F4(22n+1) were constructed by Ree (1961), who showed that they are simple if n ≥ 1. The first member of this series 2F4(2) is not simple. It was studied by Jacques Tits (1964) who showed that it is almost simple, its derived subgroup 2F4(2)′ of index 2 being a new simple group, now called the Tits group. The group...
Miriam Butt is Professor of Linguistics and Chair of the Department of Linguistics (Fachbereich Sprachwissenschaft) at the University of Konstanz. She is best known for her theoretical linguistic work on complex predicates and on grammatical case, and for her computational linguistic work in large-scale grammar development within the ParGram project.
Butt earned her doctorate in linguistics in 1993 at Stanford University. She subsequently held research and teaching positions at the Institut für Maschinelle Sprachverarbeitung at the University of Stuttgart, University of Manchester Institute of...
In mathematics, the Tits alternative, named for Jacques Tits, is an important theorem about the structure of finitely generated linear groups.
== Statement ==
The theorem, proven by Tits, is stated as follows.
Let
G
{\displaystyle G}
be a finitely generated linear group over a field. Then two following possibilities occur:
either
G
{\displaystyle G}
is virtually solvable (i.e. has a solvable subgroup of finite index)
or it contains a nonabelian free group (i.e. it has a subgroup isomorphic to the free group...
