Geodesic
On the product decomposition conjecture for finite simple groups
Nick Gill1 ; László Pyber2 ; Ian Short1 ; Endre Szabó2
1Open University, Milton Keynes, UK
2Hungarian Academy of Sciences, Budapest, Hungary
Groups, geometry, and dynamics, Tome 7 (2013) no. 4, pp. 867-882

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DOI

We prove that if G is a finite simple group of Lie type and S is a subset of G of size at least two, then G is a product of at most clog∣G∣/log∣S∣ conjugates of S, where c depends only on the Lie rank of G. This confirms a conjecture of Liebeck, Nikolov and Shalev in the case of families of simple groups of bounded rank. We also obtain various related results about products of conjugates of a set within a group.
DOI : 10.4171/ggd/208
Classification : 20-XX
Mots-clés : Conjugacy, Doubling Lemma, Product Theorem, simple group, width

Nick Gill  1   ; László Pyber  2   ; Ian Short  1   ; Endre Szabó  2

1 Open University, Milton Keynes, UK
2 Hungarian Academy of Sciences, Budapest, Hungary 
Nick Gill; László Pyber; Ian Short; Endre Szabó. On the product decomposition conjecture for  finite simple groups. Groups, geometry, and dynamics, Tome 7 (2013) no. 4, pp. 867-882. doi: 10.4171/ggd/208
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