FINITELY CONSTRAINED GROUPS OF MAXIMAL HAUSDORFF DIMENSION
2015 ◽
Vol 100
(1)
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pp. 108-123
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We prove that if $G_{P}$ is a finitely constrained group of binary rooted tree automorphisms (a group binary tree subshift of finite type) defined by an essential pattern group $P$ of pattern size $d$, $d\geq 2$, and if $G_{P}$ has maximal Hausdorff dimension (equal to $1-1/2^{d-1}$), then $G_{P}$ is not topologically finitely generated. We describe precisely all essential pattern groups $P$ that yield finitely constrained groups with maximal Hausdorff dimension. For a given size $d$, $d\geq 2$, there are exactly $2^{d-1}$ such pattern groups and they are all maximal in the group of automorphisms of the finite rooted regular tree of depth $d$.
2013 ◽
Vol 23
(01)
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pp. 69-79
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1976 ◽
Vol 1
(4)
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pp. 335-343
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2002 ◽
Vol 02
(04)
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pp. 599-607
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Keyword(s):
2008 ◽
Vol 28
(4)
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pp. 1135-1143
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Keyword(s):
1998 ◽
Vol 18
(5)
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pp. 1097-1114
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1997 ◽
Vol 17
(2)
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pp. 417-433
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