On growth of random groups of intermediate growth

Benli M. G., Grigorchuk R., Vorobets Y.

GROUPS GEOMETRY AND DYNAMICS, cilt.8, sa.3, ss.643-667, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 3
  • Basım Tarihi: 2014
  • Doi Numarası: 10.4171/ggd/243
  • Dergi Adı: GROUPS GEOMETRY AND DYNAMICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.643-667
  • Anahtar Kelimeler: Group of intermediate growth, space of finitely generated groups, generic property, random group, oscillating growth, TORSION, SPACE
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

We study the growth of typical groups from the family of p-groups of intermediate growth constructed by the second author. We find that, in the sense of category, a generic group exhibits oscillating growth with no universal upper bound. At the same time, from a measure-theoretic point of view (i.e., almost surely relative to an appropriately chosen probability measure), the growth function is bounded by e(n alpha) for some alpha < 1.