Subnormal subgroups in free groups, their growth and cogrowth

In this paper, the author (1) compare subnormal closures of finite sets in a free group F; (2) obtains the limit for the series of subnormal closures of a single element in F; (3) proves that the exponential growth rate (exp.g.r.) $\lim_{n\to \infty}\sqrt[n]{g_H(n)}$ , where gH (n) is the growth fun...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2017-11, Vol.163 (3), p.499-531
Main Author: OLSHANSKII, A. YU
Format: Article
Language:English
Subjects:
Closures
Subgroups
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Summary:In this paper, the author (1) compare subnormal closures of finite sets in a free group F; (2) obtains the limit for the series of subnormal closures of a single element in F; (3) proves that the exponential growth rate (exp.g.r.) $\lim_{n\to \infty}\sqrt[n]{g_H(n)}$ , where gH (n) is the growth function of a subgroup H with respect to a finite free basis of F, exists for any subgroup H of the free group F; (4) gives sharp estimates from below for the exp.g.r. of subnormal subgroups in free groups; and (5) finds the cogrowth of the subnormal closures of free generators.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004117000081