# On exponential growth rates for free groups.

Publicacions Matemàtiques (1998)

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

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topKoubi, 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 < 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.},

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 < 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.

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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