Gretchen Ostheimer

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Many fundamental problems are undecidable for innnite matrix groups. Polycyclic matrix groups represent a large class of groups for which these same problems are known to be decidable. In this paper we describe a suite of new algorithms for studying polycyclic matrix groups | algorithms for testing membership and for uncovering the polycyclic structure of(More)
Let K be a number eld. We present several algorithms for working with polycyclic-by-nite subgroups of GL(n; K). Let G be a subgroup of GL(n; K) given by a nite generatingset of matrices. We describe an algorithm for deciding whether or not G is polycyclic-by-nite. For polycyclic-by-nite G, we describe an algorithm for deciding whether or not a given matrix(More)
a r t i c l e i n f o a b s t r a c t MSC: 20F65 68Q15 Keywords: Logspace algorithm Logspace normal form Logspace embeddable Wreath product Baumslag–Solitar group Logspace word problem We consider the class of finitely generated groups which have a normal form computable in logspace. We prove that the class of such groups is closed under passing to finite(More)
We describe a new algorithm for nding matrix representations for polycyclic groups given by nite presentations. In contrast to previous algorithms, our algorithm is eecient enough to construct representations for some interesting examples. The examples which we studied included a collection of free nilpotent groups, and our results here led us to a(More)
We consider the class of finitely generated groups which have a normal form computable in logspace. We prove that the class of such groups is closed under passing to finite index subgroups, direct products, wreath products , and certain free products and infinite extensions, and includes the solv-able Baumslag-Solitar groups, as well as non-residually(More)