Isoperimetric inequalities for nilpotent groups

Isoperimetric inequalities for nilpotent groups

We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear upper bound on its filling length function. 1991 Mathematics Subject Classification: 20F05, 20F32, 57M07

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

Isoperimetric inequalities for soluble groups

We approach the question of which soluble groups are automatic. We describe a class of nilpotent-by-abelian groups which need to be studied in order to answer this question. We show that the nilpotent-by-cyclic groups in this class have exponential isoperimetric inequality and so cannot be automatic.

Filling Inequalities for Nilpotent Groups

We give methods for bounding the higher-order filling functions of a homogeneous nilpotent group and apply them to a family of quadratically presented groups constructed by S. Chen[9]. We find sharp bounds on some higher-order filling invariants of these groups. In particular, we show that groups with arbitrarily large nilpotency class can have euclidean n-dimensional filling volume and give an...

Isoperimetric Functions of Amalgamations of Nilpotent Groups

We consider amalgamations of nitely generated nilpotent groups of class c. We show that doubles satisfy a polynomial isoperimetric inequality of degree 2c. Generalising doubles we introduce non-twisted amalgamations and show that they satisfy a polynomial isoperimetric inequality as well. We give a su cient condition for amalgamations along abelian subgroups to be non-twisted and thereby to sat...