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Verbal width in anabelian groups

Abstract:

The class A of anabelian groups is defined as the collection of finite groups without abelian composition factors. We prove that the commutator word [x1, x2] and the power word x1p have bounded width in A when p is an odd integer. By contrast, the word x30 does not have bounded width in A. On the other hand, any given word w has bounded width for those groups G ∈ A whose composition factors are sufficiently large as a function of w. In the course of the proof we establish that sufficiently la...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s11856-016-1430-6

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Institution:
University of Oxford
Oxford college:
University College
Role:
Author
Engineering and Physical Sciences Research Council More from this funder
Publisher:
Springer Publisher's website
Journal:
Israel Journal of Mathematics Journal website
Volume:
216
Issue:
2
Pages:
847-876
Publication date:
2016-11-23
Acceptance date:
2016-01-05
DOI:
EISSN:
1565-8511
ISSN:
0021-2172
Source identifiers:
446318
Keywords:
Pubs id:
pubs:446318
UUID:
uuid:b974eda1-368e-478f-b49f-d2be3fca2802
Local pid:
pubs:446318
Deposit date:
2017-06-04

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