# Minimality of topological matrix groups and Fermat primes

`2022-03-09 10:30:00``2022-03-09 11:30:00``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``Third floor seminar room, Mathematics building, and on Zoom. See link below.``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`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

Last Updated Date : 23/02/2022