Non virtually solvable subgroups of mapping class groups have non virtually solvable representations

D ec 1 99 7 Solvable subgroups of Out ( F n ) are virtually abelian

Let Fn denote a free group of rank n. The group Out(Fn) contains mapping class groups of compact surfaces and maps onto GL(n,Z). It is perhaps not surprising that Out(Fn) behaves at times like a mapping class group and at times like a linear group. J. Birman, A. Lubotzky, and J. McCarthy [BLM83] showed that solvable subgroups of mapping class groups are finitely generated and virtually abelian....

Abelian and Solvable Subgroups of the Mapping Class Group Joan

Non-solvable Groups of Morley Rank 3

Groups of finite Morley rank have been studied by several model theorists since the early 1970s. Cherlin conjectured (see [Chl]) that infinite simple groups of finite Morley rank are algebraic groups over an algebraically closed field. This conjecture seems to be one of the most difficult problems in applied model theory. Important contributions were made by Zil’ber [Zi] and Thomas [Thl]. An En...

Good Representations and Solvable Groups

The purpose of this paper is to provide a characterization of solvable linear algebraic groups in terms of a geometric property of representations. Representations with a related property played an important role in the proof of the equivariant Riemann-Roch theorem [EG2]. In that paper, we constructed representations with that property (which we call freely good) for the group of upper triangul...

A-Generated Subgroups of A-Solvable Groups

In the discussion of A-solvable groups, the question arises if a torsion-free abelian group A of finite rank is flat as a module over its endomorphism ring if every A-generated subgroup of a torsion-free A-solvable group is A-solvable. This paper gives a negative answer by constructing a torsion-free group of rank 3 for which all A-generated torsion-free groups are A-solvable, although A is not...