Susan Hermiller Brief Summaries of Selected Research Publications

نویسنده

  • Susan Hermiller
چکیده

The set of finitely generated subgroups of the group PL+(I) of orientation-preserving piecewiselinear homeomorphisms of the unit interval includes many important groups, most notably R. Thompson’s group F . In this paper we show that every finitely generated subgroup G < PL+(I) is either soluble, or contains an embedded copy of Brin’s group B, a finitely generated, non-soluble group, which verifies a conjecture of the first author from 2009. In the case that G is soluble, we show that the derived length of G is bounded above by the number of G-orbit classes of the breakpoints of any finite set of generators. Finally, we specify a set of ‘computable’ subgroups of PL+(I) (which includes R. Thompson’s group F ) and we give an algorithm which determines in finite time whether or not any given finite subset X of such a computable group generates a soluble group. When the group is soluble, the algorithm also determines the derived length of 〈X〉.

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The Simple TimesTM

The Simple Times is an openly-available publication devoted to the promotion of the Simple Network Management Protocol (SNMP). In each issue, The Simple Times presents: a refereed technical article, an industry comment, and several featured columns. In addition, some issues include brief announcements, summaries of recent publications, and an activities calendar. For information on submissions,...

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The Simple TimesTM

The Simple Times is an openly-available publication devoted to the promotion of the Simple Network Management Protocol (SNMP). In each issue, The Simple Times presents: a refereed technical article, an industry comment, and several featured columns. In addition, some issues include brief announcements, summaries of recent publications, and an activities calendar. For information on submissions,...

متن کامل

The Simple TimesTM

The Simple Times is an openly-available publication devoted to the promotion of the Simple Network Management Protocol (SNMP). In each issue, The Simple Times presents: a refereed technical article, an industry comment, and several featured columns. In addition, some issues include brief announcements, summaries of recent publications, and an activities calendar. For information on submissions,...

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تاریخ انتشار 2015