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SEMINAR: Groups and Combinatorics Seminar: Sabina Pannek, 4pm March 12

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Today's date is Monday, March 08, 2021
Groups and Combinatorics Seminar: Sabina Pannek, 4pm March 12 Other events...
Speaker: Sabina Pannek

Title: Elements with large irreducible submodules contained in maximal subgroups of the general linear group

Time and place: 4pm Tuesday 12 Mar 2019, Blakers LT

Abstract: We refer to an element of the finite general linear group GL(V) as being fat if it leaves invariant, and acts irreducibly on, a subspace of dimension greater than dim(V)/2. Fat elements generalise the concept of ppd-elements, which are defined by the property of having orders divisible by certain primes called primitive prime divisors. In 1997, Guralnick, Penttila, Praeger and Saxl classified all subgroups of GL(V) containing ppd-elements. Their work has had a wide variety of applications in computational group theory, number theory, permutation group theory, and geometry. Our overall goal is to carry out an analogous classification of all subgroups of GL(V) containing fat elements.

During my PhD candidature I examined the occurrence of fat elements in GL(V) and various of its maximal subgroups. I showed that, often, this problem can be handled in a uniform way by considering "extremely fat" elements and counting certain irreducible polynomials. In my talk, I will present this method for groups belonging to Aschbacher's C2 class. The results we obtain significantly differ from the findings of the ppd-classification.
Contact Stephen Glasby <[email protected]>
Start Tue, 12 Mar 2019 16:00
End Tue, 12 Mar 2019 17:00
Submitted by Stephen Glasby <[email protected]>
Last Updated Wed, 10 Apr 2019 09:04
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