8 research outputs found
Palindromic Width of Wreath Products
We show that the wreath product of any finitely
generated group with has finite palindromic width. We also
show that has finite palindromic width if has finite commutator
width and is a finitely generated infinite abelian group. Further we prove
that if is a non-abelian group with finite palindromic width and any
finitely generated group, then every element of the subgroup can be
expressed as a product of uniformly boundedly many palindromes. From this we
obtain that has finite palindromic width if is a perfect group
and further that has finite palindromic width for any finite,
non-abelian group .Comment: 10 pages, 1 figur
Conjugacy Growth and Conjugacy Width of Certain Branch Groups
The conjugacy growth function counts the number of distinct conjugacy classes
in a ball of radius . We give a lower bound for the conjugacy growth of
certain branch groups, among them the Grigorchuk group. This bound is a
function of intermediate growth. We further proof that certain branch groups
have the property that every element can be expressed as a product of uniformly
boundedly many conjugates of the generators. We call this property bounded
conjugacy width. We also show how bounded conjugacy width relates to other
algebraic properties of groups and apply these results to study the palindromic
width of some branch groups.Comment: Final version, to appear in IJA