Groups with bounded generation: old and new

Groups with bounded generation: old and new

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Andrei Rapinchuk, University of Virginia

Zoom link:  https://princeton.zoom.us/j/97126136441

Passcodethe three digit integer that is the cube of the sum of its digits

A group is said to have bounded generation (BG) if it is a finite product of cyclic subgroups. We will survey the known examples of groups with (BG) and their properties. We will then report on a recent result (joint with P. Corvaja, J. Ren and U. Zannier) that non-virtually abelian anisotropic linear groups (i. e. those consisting entirely of semi-simple elements) are not boundedly generated. The proofs rely on number-theoretic techniques.