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Stable Torsion Length.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Stable Torsion Length./
Author:	Avery, Chloe I.
Description:	1 online resource (69 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 83-10, Section: B.
Contained By:	Dissertations Abstracts International83-10B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798209937425

Stable Torsion Length.
Avery, Chloe I.

Stable Torsion Length. - 1 online resource (69 pages)

Source: Dissertations Abstracts International, Volume: 83-10, Section: B.

Thesis (Ph.D.)--The University of Chicago, 2022.

Includes bibliographical references

The stable torsion length in a group is the stable word length with respect to the set of all torsion elements. We show that the stable torsion length vanishes in crystallographic groups. We then give a linear programming algorithm to compute a lower bound for stable torsion length in free products of groups. Moreover, we obtain an algorithm that exactly computes stable torsion length in free products of finite abelian groups. The nature of the algorithm shows that stable torsion length is rational in this case. As applications, we give the first exact computations of stable torsion length for nontrivial examples.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798209937425Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

AlgebraIndex Terms--Genre/Form:

554714
Electronic books.

Stable Torsion Length.
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100 1 $a Avery, Chloe I. $3 1474035
245 1 0 $a Stable Torsion Length.
264 0 $c 2022
300 $a 1 online resource (69 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 83-10, Section: B.
500 $a Advisor: Farb, Benson.
502 $a Thesis (Ph.D.)--The University of Chicago, 2022.
504 $a Includes bibliographical references
520 $a The stable torsion length in a group is the stable word length with respect to the set of all torsion elements. We show that the stable torsion length vanishes in crystallographic groups. We then give a linear programming algorithm to compute a lower bound for stable torsion length in free products of groups. Moreover, we obtain an algorithm that exactly computes stable torsion length in free products of finite abelian groups. The nature of the algorithm shows that stable torsion length is rational in this case. As applications, we give the first exact computations of stable torsion length for nontrivial examples.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
653 $a Algebra
653 $a Geometric group theory
653 $a Geometry
653 $a Mathematics
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The University of Chicago. $b Mathematics. $3 1180611
773 0 $t Dissertations Abstracts International $g 83-10B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28961919 $z click for full text (PQDT)