Stallings Foldings and Subgroups of Free Groups

Kapovich, Ilya; Myasnikov, Alexei

doi:10.1006/jabr.2001.9033

Cited by 206 publications

(411 citation statements)

References 41 publications

(58 reference statements)

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“…The algorithmic constructions involved in the computation of this invariant actually appeared in recent years, in three completely independent papers [20], [11] and [7], where the same notion was invented in independent ways. In chronological order, we refer:…”

Section: Introductionmentioning

confidence: 99%

“…• to the algebraic extensions constructed in 2002 by Kapovich and Miasnikov (see [7]), in the context of a paper where the authors surveyed, clarified and extended the list of Stallings graphical techniques.…”

Section: Introductionmentioning

confidence: 99%

“…. , n. The original proof was combinatorial, while the proof provided in [20], [11] and [7] (which is the same up to technical details) is graphical, algorithmic, simpler and more natural.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this paper is to unify the points of view in [20], [11] and [7], and to systematize the study of the concept of algebraic extensions in free groups. We show how algebraic extensions intervene in the computation of certain abstract closure properties for subgroups, sometimes making these properties decidable.…”

Section: Introductionmentioning

confidence: 99%

“…

AbstractThe aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001and Kapovich and Miasnikov 2002, where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical field-theoretic notions, and we discuss in detail the notion of algebraic closure.

…”

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confidence: 97%

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Algebraic Extensions in Free Groups

Miasnikov

Ventura

Weil

2007

Geometric Group Theory

106

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The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001and Kapovich and Miasnikov 2002, where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical field-theoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations. *

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…

…”

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Algebraic Extensions in Free Groups

Miasnikov

Ventura

Weil

2007

Geometric Group Theory

106

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An integrated electrical drive control laboratory: Speed control of induction motors

Dandil

2012

Comp Applic In Engineering

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This paper presents an integrated environment for speed control of vector controlled induction motor (IM) including simulation and experimental study. In the prepared integrated environment, students and researchers can realise the speed control of IM by selecting the classical controllers such as proportional þ integral þ derivative (PID) and integral þ proportional (IP) or intelligent controllers such as fuzzy (FC), neural network (NNC) and neuro-fuzzy (NFC). Users can perform simulation and experimental studies on-line to evaluate performance of the control system under parameter and load variations in IM drive. The integrated environment allows users to compare simulation and experimental results and evaluate basic distinctions between classical and intelligent controllers. Furthermore, performance of the controller designed by the user can be tested on-line. Important variables of drive system can be monitored as graphically or saved as digitally for further processing by using the designed graphical user interface (GUI). ß

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Recent study advances in the Department of Polymer Science and Engineering at Zhejiang University

Dong

Gao

2022

Journal of Polymer Science

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The polymer science at Zhejiang University (ZJU) is well known for its foremost origin of study and education of polymers in China. According to the latest US News rankings, it is ranked third in the subject of Polymer Sciences. The Department of Polymer Science and Engineering (DPSE) is one of the earliest academic institutions devoted to polymers at ZJU. Under the leadership of Prof. Zhi-Quan Shen and Prof. Jia-Chong Shen, academicians of the Academia Sinica, 54 faculty members (including 28 professors, 26 associate professors, and senior researchers) are now working in education and scientific research of polymer sciences, polymer composites and biomedical macromolecules. Our faculty is among the finest all over the nation, leading polymer science and engineering research. Our department has been developed as a collaborative community of faculties, students, and alumni dedicated to research developments and solving important technical questions with three decades of endeavors.In this special issue of ZJU, we aim to share a selection of recent research activities from our faculties, students, and alumni, classified into the following six topics: controlled polymerization, polymer physics and rheology, biomedical polymers, polymer membranes and films, organic and polymeric photo-electronic functional materials, and aggregationinduced emission (AIE) and graphene materials.The topic of controlled polymerization illustrates the fabrication of fine polymers with sophisticated polymerization techniques. A protocol of using readily available raw materials of ethylene oxide, propylene oxide, and carbonyl sulfide is developed by Zhang et al. to synthesize sulfur-rich poly(thioether)s that exhibit T m values ranging from 76 C to 144 C and have high refractive index up to 1.68. Du et al. synthesize a series of ABCBA symmetrical amphiphilic pentablock terpolymers with various block lengths two-step atom transfer radical polymerization. These polymers can form high-genus vesicles in dilute aqueous solutions. In another study, Ling et al. design the synthesis of P(EVL-alt-EDT)-g-PEG combining thiol-ene click polymerization and ring-opening grafting reaction. The obtained polymers consist of a hydrophobic backbone of alternative copolymers of disubstituted

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Stallings Foldings and Subgroups of Free Groups

Abstract: We re-cast in a more combinatorial and computational form the topological approach of J. Stallings to the study of subgroups of free groups.  2002 Elsevier Science (USA)

Cited by 206 publications

References 41 publications

Algebraic Extensions in Free Groups

Algebraic Extensions in Free Groups

An integrated electrical drive control laboratory: Speed control of induction motors

Recent study advances in the Department of Polymer Science and Engineering at Zhejiang University

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