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On the Asymptotics of the Growth of 2‐Step Nilpotent Groups
Author(s) -
Stoll Michael
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006371
Subject(s) - nilpotent , mathematics , nilpotent group , pure mathematics , central series , group (periodic table) , generating set of a group , function (biology) , set (abstract data type) , degree (music) , combinatorics , computer science , physics , geometry , quantum mechanics , evolutionary biology , acoustics , biology , programming language
Pansu has shown that the growth function of every virtually nilpotent group Γ with respect to any finite generating set has asymptotics γ( n )∼α n d , where d is the degree of growth of Γ. The paper refines his result in the special case of 2‐step nilpotent groups to obtain γ( n )=α n d + O ( n d −1 ).
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