Conjugacy growth and width of certain branch groups
2014 ◽
Vol 24
(08)
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pp. 1213-1231
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Keyword(s):
The conjugacy growth function counts the number of distinct conjugacy classes in a ball of radius n. 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 prove 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.
2001 ◽
Vol 11
(01)
◽
pp. 73-88
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Keyword(s):
2004 ◽
Vol 14
(05n06)
◽
pp. 677-702
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Keyword(s):
1979 ◽
Vol 80
(1)
◽
pp. 253-254
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Keyword(s):