Words and mixing times in finite simple groups | Zendy

Gili Schul | Zendy; Aner Shalev | Zendy

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Words and mixing times in finite simple groups

Author(s) -

Gili Schul,

Aner Shalev

Publication year - 2011

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/137

Subject(s) - mathematics , simple (philosophy) , mixing (physics) , simple group , classification of finite simple groups , pure mathematics , group of lie type , group theory , physics , philosophy , epistemology , quantum mechanics

Let w ¤ 1 be a non-trivial group word, let G be a finite simple group, and let w.G/ be the set of values of w in G. We show that if G is large, then the random walk on G with respect to w.G/ as a generating set has mixing time 2. This strengthens various known results, for example the fact that w.G/ covers almost all of G. Mathematics Subject Classification (2010). 20D06, 20P99.

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