Geodesic
Numerical invariants of exponential groups and locally free approximation of the braid group
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 51-63

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We continue the studying of the numerical constants of the countable groups, like entropy, escape and logariphmic volume. We give examples of the groups for which fundamental inequality is strict. 
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     author = {A. M. Vershik},
     title = {Numerical invariants of exponential groups and locally free approximation of the braid group},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {51--63},
     publisher = {mathdoc},
     volume = {266},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a4/}
}
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A. M. Vershik. Numerical invariants of exponential groups and locally free approximation of the braid group. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 51-63. http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a4/