Benjamin Blanchette, here at UQAM, has just started a math blog. He will be beginning his master’s studies in september under the supervision of Christophe Reutenauer. At least until then, he’s writing about automatic groups and geometric group theory.
What are automatic groups?
Let be a group with a finite generating set . Any element of can be represented by a string of characters using the elements of and their inverses as letters. If the group , with this specified generating set , is automatic, then an automata can determine precisely when two such character strings represent the same element of .
Thus automatic groups admit a representation as character strings that is particularily easy to work with on a computer.
But I’m not an expert and there’s much more to it. Go check out bbgrouptheory.blogspot.com!