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Homomorphisms from automorphism groups of free groups

Abstract:

The automorphism group of a finitely generated free group is the normal closure of a single element of order 2. If $m$ is less than $n$ then a homomorphism $Aut(F_n)\to Aut(F_m)$ can have cardinality at most 2. More generally, this is true of homomorphisms from $\Aut(F_n)$ to any group that does not contain an isomorphic copy of the symmetric group $S_{n+1}$. Strong constraints are also obtained on maps to groups that do not contain a copy of $W_n= (\Bbb Z/2)^n\rtimes S_n$, or of $\Bbb Z^{n-1...

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Publication status:
Published

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Publisher copy:
10.1112/S0024609303002248

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Vogtmann, K More by this author
Journal:
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
Volume:
35
Issue:
6
Pages:
785-792
Publication date:
2002-09-16
DOI:
EISSN:
1469-2120
ISSN:
0024-6093
URN:
uuid:971eee11-7b1b-41a5-9829-30d6ee70357f
Source identifiers:
14379
Local pid:
pubs:14379
Language:
English
Keywords:

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