Pure Colloquium Seminar - Schreier subgroup theorem and its generalisations, Yuri Bahturin (Newfoundland) Seminar

Event details

The rank of a subgroup of finite index in a finitely generated free group is given by the classical Schreier's formula. We start this talk with a result, joint with Alexander Olshansky, providing a formula in the case where the index is not finite. Then we turn our attention to other situations in Algebra, where the analogues of Schreier' s Freedom Theorem hold, like Lie algebras and modules over free group algebras. We will see that also in these cases one can write some formulas for the ranks of free subalgebras. These are due to Jacques Lewin and Victor Petrogradsky.