Notes on Uniform Exponential Growth and Tits Alternative
نویسنده
چکیده
Remark 1.2. Uniform exponential growth for solvable non-virtually nilpotent groups was proved independently by Osin and byWilson. The existence of a uniform constant C(d) as in Theorem 1.1 for solvable groups is very striking since it implies the well known Lehmer conjecture concerning the Mahler measure of algebraic integers. However for virtually solvable non-virtually nilpotent groups we only obtained the analog uniform result for discrete subgroups of GLd(k) were k is a local field. The details of this result will appear elsewhere.
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