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Isoperimetric Inequalities in Nilpotent Groups
Author(s) -
Pittet Christophe
Publication year - 1997
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/s0024610797005140
Subject(s) - isoperimetric inequality , nilpotent , mathematics , nilpotent group , central series , bounded function , class (philosophy) , pure mathematics , function (biology) , combinatorics , integer (computer science) , group (periodic table) , discrete mathematics , mathematical analysis , computer science , physics , quantum mechanics , artificial intelligence , evolutionary biology , biology , programming language
To each finitely generated nilpotent group Γ, we associate an integer d and show that the 2‐dimensional isoperimetric function (the Dehn function) of Γ is bounded below by a polynomial function of degree d . In the case of free nilpotent groups of class c we find (if we exclude Z) that d = c +1.