On finite groups as products of normal subsets

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• 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^{k = G for any integer k at least c·(log |G|/ log |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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