SEMINAR: Groups and Combinatorics Seminar: Marvin Krings, 4pm Nov 23 in Robert Street LT


Groups and Combinatorics Seminar: Marvin Krings, 4pm Nov 23 in Robert Street LT 
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Speaker: Marvin Krings (RWTH, Aachen)
Title: The ppart of the order of an almost simple group of Lie type
Time and place: 4pm Friday 23 Nov 2018, Robert Street LT (not Weatherburn LT)
Abstract: Primitive permutation groups are fundamental building blocks in the sense that every finite permutation group can be built from the primitive ones. Apart from the alternating group A_n and the symmetric group S_n of degree n, the primitive subgroups G of S_n are small. For example, in 1980 Praeger and Saxl showed that G e 4^n, which is much smaller than n!/2. Since this time, powerful results such as the O’NanScott Theorem, which classifies the primitive permutation groups, and the Classification of the Finite Simple Groups, have become available. We will bound the ppart G_p of G for some prime p. This is, the largest ppower p^{
u_p(G)} that divides G. The bound G e 4^n implies nu_p(G) e n og_p(4). We prove the stronger bound nu_p(G) e frac{2sqrt{n}}{(p1)}+1 (with five exceptions). For several cases, we even obtain a bound that is logarithmic in n. Our proof uses the O'NanScott theorem to reduce to simple groups. The hardest case, and the one I will discuss, is when the simple group is of Lie type.
Contact 
Stephen Glasby
<[email protected]>

Start 
Fri, 23 Nov 2018 16:00

End 
Fri, 23 Nov 2018 17:00

Submitted by 
Stephen Glasby <[email protected]>

Last Updated 
Tue, 20 Nov 2018 10:51

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