Minimality of topological matrix groups and Fermat primes

Our aim is to study topological minimality of some natural matrix groups. We show that the special upper triangular group SUT(n, F) is minimal for every local field F of characteristic distinct from 2. This result is new even for the field R of reals and it leads to some important consequences. We prove criteria for the

minimality and total minimality of the special linear group SL(n, F), where F is a subfield of a local field. One of our main applications is a characterization of

Fermat primes, which asserts that for an odd prime p the following conditions are equivalent:

(1) p is a Fermat prime;

(2) SL(p − 1,Q) is minimal, where Q is the field of rationals equipped with the

p-adic topology;

(3) SL(p − 1,Q(i)) is minimal, where Q(i) ⊂ C is the Gaussian rational field.

https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062