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Manchester Algebra Seminar - Mandi Schaeffer Fry - Galois Action on the Principal Block and Generation of Sylow Subgroups

Dates:5 May 2020
Times:16:00 - 17:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, Current University students
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  • Department of Mathematics

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  • In group "(Maths) Algebra"
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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.

Time: 4pm

Note the later time of 4pm due to time zones.

Place: Zoom

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Kieran Calvert

kieran.calvert@manchester.ac.uk

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