@article{bou-rabee_extremal_2015,
	title = {Extremal behavior of divisibility functions},
	volume = {175},
	issn = {0046-5755, 1572-9168},
	url = {http://link.springer.com/10.1007/s10711-014-9955-5},
	doi = {10.1007/s10711-014-9955-5},
	abstract = {In this short article, we study the extremal behavior F (n) of divisibility functions D introduced by the first author for finitely generated groups . These functions aim at quantifying residual finiteness and bounds give a measurement of the complexity in verifying a word is non-trivial. We show that finitely generated subgroups of GL(m, K ) for an infinite field K have at most polynomial growth for the function F (n). Consequently, we obtain a dichotomy for the growth rate of log F (n) for finitely generated subgroups of GL(n, C). We also show that if F (n) log log n, then is finite. In contrast, when contains an element of infinite order, log n F (n). We end with a brief discussion of some geometric motivation for this work.},
	language = {en},
	number = {1},
	urldate = {2021-08-11},
	journal = {Geometriae Dedicata},
	author = {Bou-Rabee, Khalid and McReynolds, D. B.},
	month = apr,
	year = {2015},
	note = {tex.ids= Bou-RabeeMcReynolds2015Extremal
publisher: Springer},
	pages = {407--415},
}

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