University of Birmingham > Talks@bham > Algebra seminar > On ﬁnite groups as products of normal subsets

## On ﬁnite groups as products of normal subsetsAdd to your list(s) Download to your calendar using vCal - Attila Maroti (Alfréd Rényi Institute of Mathematics)
- Thursday 25 June 2020, 16:00-17:00
- https://bham-ac-uk.zoom.us/j/92610684996?pwd=K2FKV2dpczhXSUdvUllqNnlYMVlEUT09.
If you have a question about this talk, please contact Chris Parker. Let G be a non-abelian ﬁnite simple group. A famous result of Liebeck and Shalev is that there is an absolute positive constant c such that whenever S is a non-trivial normal subset in G then S In the ﬁrst part of the talk this result will be generalized by showing that there exists an absolute positive constant c such that whenever S_1,\dots ,S_k are normal subsets in G with \prod_{i=1}k |S i | ≥ |G|c then S_1\dots S_k = G. This is joint work with Laci Pyber. An ingredient of the proof is that there exists a constant \delta with 0 < \delta < 1 such that if S_1 ,\dots, S_8 are normal subsets in the alternating group A_n each of size at least |A n |\delta, then S_1\dots S_8 = A_n. In the second part of the talk we will discuss how the 8 in the previous statement can be reduced to 4. This is joint work with Martino Garonzi. This talk is part of the Algebra seminar series. ## This talk is included in these lists:- Algebra seminar
- School of Mathematics events
- https://bham-ac-uk.zoom.us/j/92610684996?pwd=K2FKV2dpczhXSUdvUllqNnlYMVlEUT09
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