Non-noetherian groups without free subgroups and their group algebras (Algebraic system, Logic, Language and Related Areas in Computer Sciences II)

Abstract

Our interest is in group algebras of non-noetherian groups. In particular, we have studied about primitivity of group algebras and showed that they are often primitive if base groups have non-abelian free subgroups. Our main method includes using two edge-colored graphs. Actually, this method is effective for group algebras of groups with non-abelian free subgroups. On the other hand, there exist some important infinite groups which are non-noetherian but have no non-abelian free subgroups; e.g. Free Burnside groups and the Thompson's group F. In this talk, we first see a brief history on primitivity problem of group algebras of groups with non-abelian free subgroups. Next we introduce Thompson's group F and a problem on group algebras of it. Finally, we improve our graph theory in order to enable to investigate group algebras of Thompson's group F and apply our new graph theory to the problem.