On the product decomposition conjecture for finite simple groups | Zendy

Nick Gill | Zendy; László Pyber | Zendy; Ian Short | Zendy; Endre Szabó | Zendy

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On the product decomposition conjecture for finite simple groups

Author(s) -

Nick Gill,

László Pyber,

Ian Short,

Endre Szabó

Publication year - 2013

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/208

Subject(s) - mathematics , conjecture , simple (philosophy) , simple group , classification of finite simple groups , product (mathematics) , decomposition , pure mathematics , combinatorics , algebra over a field , discrete mathematics , group theory , group of lie type , geometry , philosophy , epistemology , ecology , biology

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 c log|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. © European Mathematical Society

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