Groups with near exponential residual finiteness growth

2015/09/04 by Bou-Rabee, Khalid, Myropolska, Aglaia · 2 citations
#20E08 #FOS: Mathematics #Group Theory (math.GR) #Primary: 20E26 #Secondary: 20F65

paper · doi:10.48550/arxiv.1509.01372

Abstract

A function ℕ → ℕ is near exponential if it is bounded above and below by functions of the form 2^nc for some c > 0. In this article we develop tools to recognize the near exponential residual finiteness growth in groups acting on rooted trees. In particular, we show the near exponential residual finiteness growth for certain branch groups, including the first Grigorchuk group, the family of Gupta-Sidki groups and their variations, and Fabrykowski-Gupta groups. We also show that the family of Gupta-Sidki p-groups, for p≥ 5, have super-exponential residual finiteness growths.

Cited by

• Residual Finiteness Growth in Virtually Nilpotent Groups
• Residual Finiteness Growth in Minimax Groups

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