Manchester Algebra Seminar - Mandi Schaeffer Fry - Galois Action on the Principal Block and Generation of Sylow Subgroups
|Starts:||16:00 5 May 2020|
|Ends:||17:00 5 May 2020|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, Current University students|
Speaker: Mandi Schaeffer Fry
Title: Galois Action on the Principal Block and Generation of Sylow Subgroups
Abstract: We show that the character table (in fact, we only require the principal block) of a finite group G determines certain generation properties of a Sylow subgroup, in terms of the Galois action on characters. Specifically, in joint work with Noelia Rizo and Carolina Vallejo, we show that one can determine from the principal block whether a Sylow 2- or 3-subgroup of G is cyclic. With Gabriel Navarro, Noelia Rizo, and Carolina Vallejo, we additionally show that one can detemine whether a Sylow 2-subgroup is generated by two elements. Our proofs of these results require the use of the Classification of Finite Simple Groups and provide evidence for the so-far elusive Alperin–McKay–Navarro conjecture.
Note the later time of 4pm due to time zones.
Travel and Contact Information
Zoom - online
Alan Turing Building