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

On finite groups as products of normal subsets

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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 Sk = 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.

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