On exponential growth rates for free groups.

Malik Koubi

Publicacions Matemàtiques (1998)

  • Volume: 42, Issue: 2, page 499-507
  • ISSN: 0214-1493

Abstract

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Let Fp be a free group of rank p ≥ 2. It is well-known that, with respect to a p-element generating set, that is, a basis, the exponential growth rate of Fp is 2p-1. We show that the exponential growth rate τ of a group G with respect to a p-element generating set X is 2p-1 if and only if G is free on X; otherwise τ < 2p-1. We also prove that, for any finite generating set X of Fp which is disjoint from X-1, the exponential growth rate τ of Fp with respect to X is 2p-1 if and only if X is a basis of Fp; otherwise τ > 2p-1.

How to cite

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Koubi, Malik. "On exponential growth rates for free groups.." Publicacions Matemàtiques 42.2 (1998): 499-507. <http://eudml.org/doc/41342>.

@article{Koubi1998,
abstract = {Let Fp be a free group of rank p ≥ 2. It is well-known that, with respect to a p-element generating set, that is, a basis, the exponential growth rate of Fp is 2p-1. We show that the exponential growth rate τ of a group G with respect to a p-element generating set X is 2p-1 if and only if G is free on X; otherwise τ &lt; 2p-1. We also prove that, for any finite generating set X of Fp which is disjoint from X-1, the exponential growth rate τ of Fp with respect to X is 2p-1 if and only if X is a basis of Fp; otherwise τ &gt; 2p-1.},
author = {Koubi, Malik},
journal = {Publicacions Matemàtiques},
keywords = {Grupos libres; Factores de crecimiento; Bases topológicas; free groups; word lengths; exponential growth rates; generating sets; groups of exponential growth},
language = {eng},
number = {2},
pages = {499-507},
title = {On exponential growth rates for free groups.},
url = {http://eudml.org/doc/41342},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Koubi, Malik
TI - On exponential growth rates for free groups.
JO - Publicacions Matemàtiques
PY - 1998
VL - 42
IS - 2
SP - 499
EP - 507
AB - Let Fp be a free group of rank p ≥ 2. It is well-known that, with respect to a p-element generating set, that is, a basis, the exponential growth rate of Fp is 2p-1. We show that the exponential growth rate τ of a group G with respect to a p-element generating set X is 2p-1 if and only if G is free on X; otherwise τ &lt; 2p-1. We also prove that, for any finite generating set X of Fp which is disjoint from X-1, the exponential growth rate τ of Fp with respect to X is 2p-1 if and only if X is a basis of Fp; otherwise τ &gt; 2p-1.
LA - eng
KW - Grupos libres; Factores de crecimiento; Bases topológicas; free groups; word lengths; exponential growth rates; generating sets; groups of exponential growth
UR - http://eudml.org/doc/41342
ER -

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