POLYNOMIAL DEHN FUNCTIONS AND THE LENGTH OF ASYNCHRONOUSLY AUTOMATIC STRUCTURES

2002 ◽  
Vol 85 (2) ◽  
pp. 441-466 ◽  
Author(s):  
MARTIN R. BRIDSON
Keyword(s):  
Automorphism Group ◽  
Free Group ◽  
Dehn Function ◽  
Arbitrary Degree ◽  
Dehn Functions ◽  
Automatic Structures ◽  
Automatic Groups ◽  
Observed Behaviour ◽  
Exact Calculations ◽  
Do So

We extend the range of observed behaviour among length functions of optimal asynchronously automatic structures. We do so by means of a construction that yields asynchronously automatic groups with finite aspherical presentations where the Dehn function of the group is polynomial of arbitrary degree. Many of these groups can be embedded in the automorphism group of a free group. Moreover, the fact that the groups have aspherical presentations makes them useful tools in the search to determine the spectrum of exponents for second order Dehn functions. We contribute to this search by giving the first exact calculations of groups with quadratic and superquadratic exponents. 2000 Mathematical Subject Classification:20F06, 20F65, 20F69.

On the Geometry of the Automorphism Group of a Free Group

1995 ◽  
Vol 27 (6) ◽  
pp. 544-552 ◽  
Author(s):  
Martin R. Bridson ◽  
Karen Vogtmann
Keyword(s):  
Automorphism Group ◽  
Free Group

Linear Representations of the Automorphism Group of a Free Group

2009 ◽  
Vol 18 (5) ◽  
pp. 1564-1608 ◽  
Author(s):  
Fritz Grunewald ◽  
Alexander Lubotzky
Keyword(s):  
Automorphism Group ◽  
Free Group ◽  
Linear Representations

scholarly journals The automorphism group of the free group of rank 2 is a CAT(0) group

2010 ◽  
Vol 59 (2) ◽  
pp. 297-302 ◽  
Author(s):  
Adam Piggott ◽  
Kim Ruane ◽  
Genevieve Walsh
Keyword(s):  
Automorphism Group ◽  
Free Group ◽  
Rank 2

Finite Quotients of the Automorphism Group of a Free Group

1977 ◽  
Vol 29 (3) ◽  
pp. 541-551 ◽  
Author(s):  
Robert Gilman
Keyword(s):  
Automorphism Group ◽  
Normal Subgroup ◽  
Free Group ◽  
Outer Automorphism ◽  
Permutation Representation ◽  
Finitely Generated ◽  
Outer Automorphism Group ◽  
Finite Quotients

Let G and F be groups. A G-defining subgroup of F is a normal subgroup N of F such that F/N is isomorphic to G. The automorphism group Aut (F) acts on the set of G-defining subgroups of F. If G is finite and F is finitely generated, one obtains a finite permutation representation of Out (F), the outer automorphism group of F. We study these representations in the case that F is a free group.

scholarly journals COMPRESSED WORDS AND AUTOMORPHISMS IN FULLY RESIDUALLY FREE GROUPS

2010 ◽  
Vol 20 (03) ◽  
pp. 343-355 ◽  
Author(s):  
JEREMY MACDONALD
Keyword(s):  
Automorphism Group ◽  
Word Problem ◽  
Free Group ◽  
Polynomial Time ◽  
Free Groups ◽  
Finitely Generated

We show that the compressed word problem in a finitely generated fully residually free group ([Formula: see text]-group) is decidable in polynomial time, and use this result to show that the word problem in the automorphism group of an [Formula: see text]-group is decidable in polynomial time.

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