Alexander Olshanskii
Subgroup Distortion in Wreath Products of Cyclic Groups.
Thu, 09/23/2010 - 15:02 — SomNambulAuthors: Alexander Olshanskii, Tara Davis
Subjects: Group Theory
AbstractWe study the effects of subgroup distortion in the wreath products $Z^k wr
Z$. We show that for $k>0$ fixed, and for any polynomial, there is a
2-generated subgroup of $Z^k wr Z$ having distortion function equivalent to the
given polynomial. Moreover, every finitely generated subgroup of $Z^k wr Z$ has
distortion function bounded above by some polynomial.Filtrations and Distortion in Infinite-Dimensional Algebras.
Tue, 02/02/2010 - 16:01 — SomNambulAuthors: Yuri Bahturin, Alexander Olshanskii
Subjects: Rings and Algebras
AbstractA tame filtration of an algebra is defined by the growth of its terms, which
has to be majorated by an exponential function. A particular case is the degree
filtration used in the definition of the growth of finitely generated algebras.
The notion of tame filtration is useful in the study of possible distortion of
degrees of elements when one algebra is embedded as a subalgebra in another. A
geometric analogue is the distortion of the (Riemannian) metric of a (Lie)
subgroup when compared to the metric induced from the ambient (Lie) group.
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