The length of mixed identities for finite groups

Venue:
Geb. 20.30, SR 2.058

Date:
18.04.2024
 Speaker:

Time:
15:45 Uhr

Abstract: We prove that there exists a constant c > 0 such that any finite group having no nontrivial mixed identity of length ≤ c is an almost simple group with a simple group of Lie type as its socle. Starting the study of mixed identities for almost simple groups, we obtain results for groups with socle PSL(n,q), PSp(2m,q), PΩ^{o}(2m1,q), and PSU(n,q) for a prime power q. For such groups, we will prove rankindependent bounds for the length of a shortest nontrivial mixed identity, depending only on the field size q.
This is joint work with Henry Bradford and Andreas Thom.