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Groups with bounded verbal conjugacy classes
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Sergio Brazil
,
Alexei Krasilnikov
Published/Copyright:
May 12, 2006
Abstract
Let F be a free group and let w ∈ F. For a group G, let Gw denote the set of all w-values in G and w(G) the verbal subgroup of G corresponding to w. A word w is called boundedly concise if, for each group G such that |Gw| ≤ m, we have |w(G)| ≤ c for some integer c = c(m) depending only on m. The main theorem of the paper says that if w is a boundedly concise word and G is a group such that |xGw| ≤ m for all x ∈ G then |xw(G)| ≤ d for all x ∈ G and some integer d = d(m,w) depending only on m and w.
Received: 2004-06-28
Accepted: 2005-04-04
Published Online: 2006-05-12
Published in Print: 2006-01-26
© Walter de Gruyter
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Articles in the same Issue
- A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups
- Reduction theorems for Clifford classes
- Finite groups with NE-subgroups
- Jordan groups and limits of betweenness relations
- Quasi-finitely axiomatizable nilpotent groups
- Quasi-finitely axiomatizable groups and groups which are prime models
- The structure of Bell groups
- Groups with bounded verbal conjugacy classes
Articles in the same Issue
- A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups
- Reduction theorems for Clifford classes
- Finite groups with NE-subgroups
- Jordan groups and limits of betweenness relations
- Quasi-finitely axiomatizable nilpotent groups
- Quasi-finitely axiomatizable groups and groups which are prime models
- The structure of Bell groups
- Groups with bounded verbal conjugacy classes
