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Subnormal subgroups in free groups, their growth and cogrowth

Published online by Cambridge University Press:  27 February 2017

A. YU. OLSHANSKII
A. YU. OLSHANSKII*
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville 37240, U.S.A., and Moscow State University, Moscow 119991, Russia. e-mail: [email protected]
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 163 , Issue 3 , November 2017 , pp. 499 - 531
Copyright
Copyright © Cambridge Philosophical Society 2017 

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