# Joint IAS/Princeton University Number Theory Seminar

## Groups with bounded generation: old and new

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.

### Date & Time

May 06, 2021 | 4:30pm – 5:30pm

### Location

Remote Access### Speakers

### Additional Info

### Event Series

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### Notes

Zoom link password hint: the three digit integer that is the cube of the sum of its digits.

Video link: https://www.ias.edu/video/groups-bounded-generation-old-and-new