Groups and Dynamics Seminar

Date: March 26, 2025

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Yuri Bahturin, Memorial University of Newfoundland

Title: On the growth and cogrowth of subgroups in free groups and subalgebras in free Lie algebras

Abstract: The talk is based on the results of A. Yu. Olshanskii and the speaker. Important results about the growth and cogrowth of subgroups in free groups have been obtained by R. I. Grigorchuk. In this talk I will speak about the special features of the growth and cogrowth when the subgroups are subnormal and the subalgebras are subideals. One says that a subgroup H of a group G is subnormal if there is a descending chain of subgroups G=H_0>H_1>...>H_k=H with every term being a normal subgroup in the previous one. Similarly one defines subideals in an algebra. Thus the growth and cogrowth then give a picture intermediate between these values, say, for normal subgroups and general finitely generated subgroups.