871 research outputs found
Limits of Baumslag-Solitar groups and dimension estimates in the space of marked groups
We prove that the limits of Baumslag-Solitar groups which we previously
studied are non-linear hopfian C*-simple groups with infinitely many twisted
conjugacy classes. We exhibit infinite presentations for these groups, classify
them up to group isomorphism, describe their automorphisms and discuss the word
and conjugacy problems. Finally, we prove that the set of these groups has
non-zero Hausforff dimension in the space of marked groups on two generators.Comment: 30 pages, no figures, englis
Regular left-orders on groups
A regular left-order on finitely generated group is a total,
left-multiplication invariant order on whose corresponding positive cone is
the image of a regular language over the generating set of the group under the
evaluation map. We show that admitting regular left-orders is stable under
extensions and wreath products and give a classification of the groups all
whose left-orders are regular left-orders. In addition, we prove that solvable
Baumslag-Solitar groups admits a regular left-order if and only if
. Finally, Hermiller and Sunic showed that no free product admits a
regular left-order, however we show that if and are groups with regular
left-orders, then admits a regular left-order.Comment: 41 pages,9 figure
Linguistics
Contains research objectives and reports on four research projects.National Institutes of Health (Grant 5 TO1 HD00111-08)National Institute of Mental Health (Grant 2 P01 MH13390-06
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