Efficient bounded generation by subgroups of Q-rank one

Dave Witte Morris
University of Lethbridge

The Brown-Fisher-Hurtado proof for SL(n,Z) uses an old observation of A.Lubotzky, S.Mozes, and M.S.Raghunathan that (up to a bounded factor) the word length of every element of SL(n,Z) can be realized by a word that is the product of a bounded number of elements that are each in an obvious copy of SL(2,Z). We will describe the statement and proof of the natural generalization that is expected to play an analogous role in the proof of Zimmer's Conjecture for other noncocompact arithmetic groups. The talk will also provide an introduction to some key concepts in the study of arithmetic groups, such as Q-rank, parabolic subgroups, and the definition of the term "arithmetic group".

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