Elementary Theory of Groups and Group Rings, and Related Topics: Proceedings of the Conference held at Fairfield University and at the Graduate Center, CUNY, November 1-2, 2018

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Elementary Theory of Groups and Group Rings, and Related Topics

Proceedings of the Conference held at Fairfield University and at the Graduate Center, CUNY, November 1-2, 2018

Edited by: Paul Baginski , Benjamin Fine , Anja Moldenhauer , Gerhard Rosenberger and Vladimir Shpilrain

Language: English

Published/Copyright: 2020

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De Gruyter Proceedings in Mathematics

About this book

This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments.

A selection of up-to-date contributions in group theory and its relations with logic and cryptography
Includes works by well-known experts in the field
Of interest to mathematicians working in group theory and related areas

Author / Editor information

P. Baginski and B. Fine, Fairfield U., USA; A. Moldenhauer and G. Rosenberger, U. Hamburg, Germany; V. Shpilrain, CUNY, USA.

Topics

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Frontmatter
I

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Introduction
V

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Conference booklet and talks
VII

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Remembrances of Gilbert
XI

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Contents
XXIX

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Explicit universal axioms for Kaplansky groups
1
Sergey Bakulin and Alexei Miasnikov

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Isoperimetric and isodiametric functions of group extensions
7
Gilbert Baumslag, Martin R. Bridson and Charles F. Miller

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The homology of groups, profinite completions, and echoes of Gilbert Baumslag
11
Martin R. Bridson

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Some properties of the Baumslag groups G(m, n)
29
Anthony E. Clement

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Some model theory of the Heisenberg group: I. Unitriangular representations of models of a subtheory of its universal theory
33
Anthony M. Gaglione and Dennis Spellman

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Some model theory of the Heisenberg group: II. The three generator case
47
Anthony M. Gaglione and Dennis Spellman

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On vector-valued Hecke forms
53
Benjamin Fine, Anja I. S. Moldenhauer and Gerhard Rosenberger

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Two algorithms in group theory
73
Rita Gitik

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On products of closed subsets in free groups
81
Rita Gitik and Eliyahu Rips

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Misbehaved direct products
85
Ron Hirshon

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A survey on Albert algebras and groups of type F₄
89
Neha Hooda

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Perspectives on p-ary bent functions
103
David Joyner and Caroline Melles

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Multilinear cryptography using nilpotent groups
127
Delaram Kahrobaei, Antonio Tortora and Maria Tota

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Musings on generic-case complexity
135
Ilya Kapovich

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Noncommutative Gebauer–Möller criteria
149
Martin Kreuzer and Xingqiang Xiu

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On the numbers of the form x² + 11y²
177
Martin Kreuzer and Gerhard Rosenberger

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Separability properties of nilpotent ℚ[x]-powered groups
203
Stephen Majewicz and Marcos Zyman

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Infinite nested radicals
219
Barry B. Mittag

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Commutative transitivity property in groups and Lie algebras
225
Mohammad Reza R. Moghaddam, Gerhard Rosenberger and Mohammad Amin Rostamyari

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Simplicial subdivisions and the chromatic number of a group
233
Leonard Wienke

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

February 10, 2020

eBook ISBN:

9783110638387

Hardcover published on:

February 10, 2020

Hardcover ISBN:

9783110636734

Pages and Images/Illustrations in book

Front matter:

30

Main content:

242

Illustrations:

15

https://doi.org/10.1515/9783110638387

eBook ISBN: 9783110638387

Hardcover ISBN: 9783110636734

Keywords for this book

Gruppentheorie; Kryptologie; Logik

Audience(s) for this book

Researchers and graduate students in group theory and algebra.

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Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

Elementary Theory of Groups and Group Rings, and Related Topics

Overview

About this book

Author / Editor information

Topics

Table of contents

Frontmatter

Introduction

Conference booklet and talks

Remembrances of Gilbert

Contents

Explicit universal axioms for Kaplansky groups

Isoperimetric and isodiametric functions of group extensions

The homology of groups, profinite completions, and echoes of Gilbert Baumslag

Some properties of the Baumslag groups G(m, n)

Some model theory of the Heisenberg group: I. Unitriangular representations of models of a subtheory of its universal theory

Some model theory of the Heisenberg group: II. The three generator case

On vector-valued Hecke forms

Two algorithms in group theory

On products of closed subsets in free groups

Misbehaved direct products

A survey on Albert algebras and groups of type F4

Perspectives on p-ary bent functions

Multilinear cryptography using nilpotent groups

Musings on generic-case complexity

Noncommutative Gebauer–Möller criteria

On the numbers of the form x2 + 11y2

Separability properties of nilpotent ℚ[x]-powered groups

Infinite nested radicals

Commutative transitivity property in groups and Lie algebras

Simplicial subdivisions and the chromatic number of a group

Bibliographic data

A survey on Albert algebras and groups of type F₄

On the numbers of the form x² + 11y²