SEMINAR: Groups and Combinatorics Seminar: Proportions of elements of certain orders in classical groups


Groups and Combinatorics Seminar: Proportions of elements of certain orders in classical groups 
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Groups and Combinatorics Seminar
Simon Guest (UWA) will speak on
Proportions of elements of certain orders in classical groups
at 12 noon Tuesday 27 April in MLR2
Abstract: (joint work with Cheryl, and Tomasz Popiel)
Let G be a finite group. We say that an element g in G has 2part
order 2^j if 2^j is the largest power of 2 dividing the order of g. To analyze recognition algorithms for classical groups, we are
sometimes presented with the following question. Take the direct
product of two classical groups A x B and choose a random element
(a,b); what is the probability that (a,b) powers up to an element of the form (z,1), where z is an involution in A? We require that the 2part order of a be greater than the 2part order of b. In order to estimate this probability, we first establish lower bounds on the
proportion of elements in the symmetric group with a given 2part
order. We will describe the relationship between maximal tori in a classical group and its Weyl group. Since the Weyl group of a
classical group involves the symmetric group, we can use the lower bounds for the symmetric group, together with this relationship, to obtain corresponding lower bounds for classical groups of odd
characteristic. In fact, if A and B have dimension m and nm, and m is contained in the interval [n/3,n/2] (for example if A x B is the centralizer of a strong involution), then we show that the
probability that (a,b) powers up to (z,1) is at least an explicit
constant.
All Welcome
Speaker(s) 
Simon Guest

Location 
Maths Lecture Room 2


Contact 
Michael Giudici
<[email protected]>

Start 
Tue, 27 Apr 2010 12:00

End 
Tue, 27 Apr 2010 13:00

Submitted by 
Michael Giudici <[email protected]>

Last Updated 
Mon, 26 Apr 2010 09:00

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