You are cordially invited to the Algebra Seminar organized by the Department of Mathematics.
Speaker: Danila Revin (Sobolev Institute of Mathematics)
“The Baer-Suzuki width of a complete class of finite groups is finite”
Abstract: Let X be a nonempty class of finite groups closed under the taking subgroups, homomorphic images and extensions (the latter means that a finite group G belongs to X if there is a normal subgroup H in G such that both H and G/H belong to X). A group G is called an X-group if G∈X. According to Gordeev, Grunewald, Kunyavskiĭ, and Plotkin, the Baer-Suzuki width BS(X) of X does not exceed a non-negative integer m if, in any finite group G, the largest normal X-subgroup coincides with the set of elements x such that every m elements conjugate to x generate an X-subgroup. If there are no m for which BS(X)⩽m, then by definition BS(X)=∞. The main result of the talk states that BS(X)<∞ for every class X with the above properties. More precisely, if X is distinct from the class of all finite groups, then the value of BS(X) does not exceed max{11,2Υ+1} where Υ is equal to the largest n such that Sym(n)∈X.
Date: Wednesday, 30 April 2025
Time: 13:30
Place: Zoom
To request the event link, please send a message to d.yilmaz@bilkent.edu.tr