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Journal articles on the topic 'Group theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 July 2024

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1

Berestovskii, Valera, and Conrad Plaut. "Covering group theory for compact groups." Journal of Pure and Applied Algebra 161, no. 3 (July 2001): 255–67. http://dx.doi.org/10.1016/s0022-4049(00)00105-5.

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2

Berestovskii, Valera, and Conrad Plaut. "Covering group theory for topological groups." Topology and its Applications 114, no. 2 (July 2001): 141–86. http://dx.doi.org/10.1016/s0166-8641(00)00031-6.

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3

BROWN, F., and N. G. MAROUDAS. "Group theory." Nature 348, no. 6303 (December 1990): 669. http://dx.doi.org/10.1038/348669b0.

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4

Porter, T. "Undergraduate Projects in Group Theory: Automorphism Groups." Irish Mathematical Society Bulletin 0016 (1986): 69–72. http://dx.doi.org/10.33232/bims.0016.69.72.

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5

Gordon, Gary. "USING WALLPAPER GROUPS TO MOTIVATE GROUP THEORY." PRIMUS 6, no. 4 (January 1996): 355–65. http://dx.doi.org/10.1080/10511979608965838.

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6

Berestovskii, Valera, and Conrad Plaut. "Covering group theory for locally compact groups." Topology and its Applications 114, no. 2 (July 2001): 187–99. http://dx.doi.org/10.1016/s0166-8641(00)00032-8.

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7

Xue, Zeqi. "Group Theory and Ring Theory." Journal of Physics: Conference Series 2386, no. 1 (December 1, 2022): 012024. http://dx.doi.org/10.1088/1742-6596/2386/1/012024.

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Abstract Group theory is an important theory in abstract algebra. A ring is a kind of algebraic system with two operations (addition and multiplication). It has a deep relationship with groups, especially with the Abelian group. In this essay, the ring and the residual class ring will be talked about. Firstly, this passage is aim to talk about some basic knowledge about the ring which will let readers have a basic understanding of a ring. Then this passage will discuss the residual class ring and subring of the residual class ring of modulo. Some concepts about the ring are also mentioned, such as the centre of the ring, the identity of the ring, the classification of a ring, the residual class ring, the field and the zero divisors. The definitions of mathematical terms mentioned before are stated, as well as some examples of the part of those terms are given. In this passage, there are also some lemmas which are the properties of ring and subring. Future studies of rings and subrings can focus on the application of physics.

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8

Wang, Mingshen. "Group Theory in Number Theory." Theoretical and Natural Science 5, no. 1 (May 25, 2023): 9–13. http://dx.doi.org/10.54254/2753-8818/5/20230254.

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The theory of groups exists in many fields of mathematics and has made a great impact on many fields of mathematics. In this article, this paper first introduces the history of group theory and elementary number theory, and then lists the definitions of group, ring, field and the most basic prime and integer and divisor in number theory that need to be used in this article. Then from the definitions, step by step, Euler's theorem, Bzout's lemma, Wilson's theorem and Fermat's Little theorem in elementary number theory are proved by means of definitions of group theory, cyclic groups, and even polynomials over domains. Finally, some concluding remarks are made. Many number theory theorems can be proved directly by the method of group theory without the action of tricks in number theory. Number theory is the thinking of certain special groups (e.g., (Z,+),(Z,)), so the methods of group theory work well inside number theory.

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9

Virginia Brabender. "Chaos Theory and Group Psychotherapy 15 Years Later." Group 40, no. 1 (2016): 9. http://dx.doi.org/10.13186/group.40.1.0009.

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10

Denton, Brian, and Michael Aschbacher. "Finite Group Theory." Mathematical Gazette 85, no. 504 (November 2001): 546. http://dx.doi.org/10.2307/3621802.

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11

Eick, Bettina, Gerhard Hiß, Derek Holt, and Eamonn O’Brien. "Computational Group Theory." Oberwolfach Reports 13, no. 3 (2016): 2123–69. http://dx.doi.org/10.4171/owr/2016/37.

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12

Abért, Miklós, Damien Gaboriau, and Andreas Thom. "Measured Group Theory." Oberwolfach Reports 13, no. 3 (2016): 2347–97. http://dx.doi.org/10.4171/owr/2016/41.

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13

Clay, Matt. "Geometric Group Theory." Notices of the American Mathematical Society 69, no. 10 (November 1, 2022): 1. http://dx.doi.org/10.1090/noti2572.

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14

Kida, Yoshikata. "Ergodic group theory." Sugaku Expositions 35, no. 1 (April 7, 2022): 103–26. http://dx.doi.org/10.1090/suga/470.

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15

Whitfield, John. "Collaboration: Group theory." Nature 455, no. 7214 (October 2008): 720–23. http://dx.doi.org/10.1038/455720a.

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16

Keurentjes, Arjan. "Oxidation group theory." Classical and Quantum Gravity 20, no. 12 (May 20, 2003): S525—S531. http://dx.doi.org/10.1088/0264-9381/20/12/319.

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17

Hempel, Nadja. "Almost group theory." Journal of Algebra 556 (August 2020): 169–224. http://dx.doi.org/10.1016/j.jalgebra.2020.03.001.

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18

Eick, Bettina, Derek Holt, Gabriele Nebe, and Eamonn O'Brien. "Computational Group Theory." Oberwolfach Reports 18, no. 3 (November 25, 2022): 2027–87. http://dx.doi.org/10.4171/owr/2021/38.

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19

Roush, F. W. "Computational group theory." Mathematical Social Sciences 11, no. 1 (February 1986): 93–94. http://dx.doi.org/10.1016/0165-4896(86)90008-9.

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20

Sury, B. "Combinatorial group theory." Resonance 1, no. 11 (November 1996): 42–50. http://dx.doi.org/10.1007/bf02835212.

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21

Loewenstein, Sophie Freud. "Group Theory in an Experiential Group." Social Work with Groups 8, no. 1 (March 20, 1985): 25–40. http://dx.doi.org/10.1300/j009v08n01_04.

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22

Birget, Jean-Camille, and John Rhodes. "Group theory via global semigroup theory." Journal of Algebra 120, no. 2 (February 1989): 284–300. http://dx.doi.org/10.1016/0021-8693(89)90199-3.

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23

Knapp, A. W., Andrew Baker, and Wulf Rossmann. "Matrix Groups: An Introduction to Lie Group Theory." American Mathematical Monthly 110, no. 5 (May 2003): 446. http://dx.doi.org/10.2307/3647845.

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24

Eklof, Paul C. "Set Theory Generated by Abelian Group Theory." Bulletin of Symbolic Logic 3, no. 1 (March 1997): 1–16. http://dx.doi.org/10.2307/421194.

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Introduction. This survey is intended to introduce to logicians some notions, methods and theorems in set theory which arose—largely through the work of Saharon Shelah—out of (successful) attempts to solve problems in abelian group theory, principally the Whitehead problem and the closely related problem of the existence of almost free abelian groups. While Shelah's first independence result regarding the Whitehead problem used established set-theoretical methods (discussed below), his later work required new ideas; it is on these that we focus. We emphasize the nature of the new ideas and the historical context in which they arose, and we do not attempt to give precise technical definitions in all cases, nor to include a comprehensive survey of the algebraic results.In fact, very little algebraic background is needed beyond the definitions of group and group homomorphism. Unless otherwise specified, we will use the word “group” to refer to an abelian group, that is, the group operation is commutative. The group operation will be denoted by +, the identity element by 0, and the inverse of a by −a. We shall use na as an abbreviation for a + a + … + a [n times] if n is positive, and na = (−n)(−a) if n is negative.

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25

Burn, Bob, Walter Ledermann, and Alan J. Weir. "Introduction to Group Theory." Mathematical Gazette 81, no. 491 (July 1997): 332. http://dx.doi.org/10.2307/3619240.

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26

Canals, B., and H. Schober. "Introduction to group theory." EPJ Web of Conferences 22 (2012): 00004. http://dx.doi.org/10.1051/epjconf/20122200004.

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27

Alperin, J. L. "Book Review: Group theory." Bulletin of the American Mathematical Society 17, no. 2 (October 1, 1987): 339–41. http://dx.doi.org/10.1090/s0273-0979-1987-15583-2.

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28

Ben Geloun, Joseph. "Classical group field theory." Journal of Mathematical Physics 53, no. 2 (February 2012): 022901. http://dx.doi.org/10.1063/1.3682651.

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29

Sternberg, Shlomo, and Meinhard E. Mayer. "Group Theory and Physics." Physics Today 48, no. 6 (June 1995): 62–63. http://dx.doi.org/10.1063/1.2808071.

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30

Martin, A. D. "Group Theory in Physics." Physics Bulletin 37, no. 10 (October 1986): 426. http://dx.doi.org/10.1088/0031-9112/37/10/021.

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31

Thomas, C. B. "GROUP THEORY AND PHYSICS." Bulletin of the London Mathematical Society 29, no. 1 (January 1997): 119–20. http://dx.doi.org/10.1112/s0024609396281676.

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32

Sternberg, Shlomo, and Eugene Golowich. "Group Theory and Physics." American Journal of Physics 63, no. 6 (June 1995): 573–74. http://dx.doi.org/10.1119/1.17874.

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33

SAPIR, MARK V. "SOME GROUP THEORY PROBLEMS." International Journal of Algebra and Computation 17, no. 05n06 (August 2007): 1189–214. http://dx.doi.org/10.1142/s0218196707003925.

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This is a survey of some problems in geometric group theory that I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some necessary definitions and motivations, problems and some discussions of them. For each problem, I try to mention the author. If the author is not given, the problem, to the best of my knowledge, was formulated by me first.

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34

Bondoni, Davide. "Schröder and group theory." Lettera Matematica 2, no. 3 (August 6, 2014): 129–32. http://dx.doi.org/10.1007/s40329-014-0059-8.

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35

Gurau, Razvan. "Colored Group Field Theory." Communications in Mathematical Physics 304, no. 1 (March 8, 2011): 69–93. http://dx.doi.org/10.1007/s00220-011-1226-9.

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36

Geoghegan, Ross. "CURVATURE AND GROUP THEORY." Contributions, Section of Natural, Mathematical and Biotechnical Sciences 38, no. 2 (December 20, 2017): 147. http://dx.doi.org/10.20903/csnmbs.masa.2017.38.2.110.

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37

Tang, Dongxian, Zichang Wang, and Bangning Yue. "Applications of Group Theory." Journal of Physics: Conference Series 2381, no. 1 (December 1, 2022): 012110. http://dx.doi.org/10.1088/1742-6596/2381/1/012110.

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Abstract Groups play a fundamental role in Abstract Algebra: many algebraic structures, including rings, fields, and modules, can be seen as formed by adding new operations and axioms based on groups. Researchers often use group theory to explain many kinds of phenomena. In recent years, group theory has been introduced into crystallography to further explore the macroscopic symmetry of crystals from a mathematical point of view. In this paper, the applications of group theory in crystallography and magic cubic will be discussed. Basic definitions and models of these fields are demonstrated. A finite group is a group with a finite number of elements, which are the important contents of group theory. Besides, this paper proves that n−1 elements in a n order group can completely decide the nth element and gives a method of the nth element in a commutative group of order n. The analysis suggests that the research method of group theory has an important influence on other subjects.

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38

Leyton, Michael. "Group Theory and Architecture." Nexus Network Journal 3, no. 2 (September 2001): 39–58. http://dx.doi.org/10.1007/s00004-001-0022-9.

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39

Becker, Oren, Alexander Lubotzky, and Jonathan Mosheiff. "Testability in group theory." Israel Journal of Mathematics 256, no. 1 (September 2023): 61–90. http://dx.doi.org/10.1007/s11856-023-2503-y.

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AbstractThis paper is a journal counterpart to [5], in which we initiate the study of property testing problems concerning a finite system of relations E between permutations, generalizing the study of stability in permutations. To every such system E, a group Γ = ΓE is associated and the testability of E depends only on Γ (just like in Galois theory, where the solvability of a polynomial is determined by the solvability of the associated group). This leads to the notion of testable groups, and, more generally, Benjamini–Schramm rigid groups. The paper presents an ensemble of tools to check if a given group Γ is testable/BS-rigid or not.

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40

Jensen, David, and Kate Ponto. "Group Theory via Quilts." Mitteilungen der Deutschen Mathematiker-Vereinigung 31, no. 4 (December 9, 2023): 218–19. http://dx.doi.org/10.1515/dmvm-2023-0072.

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41

Morlin, Fernando Vinícius, Andrea Piga Carboni, and Daniel Martins. "Synthesis of Assur groups via group and matroid theory." Mechanism and Machine Theory 184 (June 2023): 105279. http://dx.doi.org/10.1016/j.mechmachtheory.2023.105279.

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42

Opolka, H. "Group Extensions and Cohomology Groups." Journal of Algebra 156, no. 1 (April 1993): 178–82. http://dx.doi.org/10.1006/jabr.1993.1068.

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43

Gonçalves, J. Z., and D. S. Passman. "Linear groups and group rings." Journal of Algebra 295, no. 1 (January 2006): 94–118. http://dx.doi.org/10.1016/j.jalgebra.2005.02.009.

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44

Arthur A. Gray. "Caring Wins Out Over Theory: A Response to Walter Stone's “Thinking About Our Work”." Group 38, no. 3 (2014): 251. http://dx.doi.org/10.13186/group.38.3.0251.

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45

Victor L. Schermer. "Back to the Future of Group Therapy Theory: 15 Years Into the New Millennium." Group 40, no. 1 (2016): 53. http://dx.doi.org/10.13186/group.40.1.0053.

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46

Capitão, Claudio Garcia. "Freud’s Theory and the Group Mind Theory: Formulations." Open Journal of Medical Psychology 03, no. 01 (2014): 24–35. http://dx.doi.org/10.4236/ojmp.2014.31003.

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47

Mj, Mahan. "Cannon–Thurston maps in Kleinian groups and geometric group theory." Surveys in Differential Geometry 25, no. 1 (2020): 281–318. http://dx.doi.org/10.4310/sdg.2020.v25.n1.a8.

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48

Lubotzky, Alexander, and Chen Meiri. "Sieve methods in group theory I: Powers in linear groups." Journal of the American Mathematical Society 25, no. 4 (2012): 1119–48. http://dx.doi.org/10.1090/s0894-0347-2012-00736-x.

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49

Fok, Chi-Kwong. "KR-theory of compact Lie groups with group anti-involutions." Topology and its Applications 197 (January 2016): 50–59. http://dx.doi.org/10.1016/j.topol.2015.10.008.

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50

Mikhailov, Roman, and Jie Wu. "Combinatorial group theory and the homotopy groups of finite complexes." Geometry & Topology 17, no. 1 (March 7, 2013): 235–72. http://dx.doi.org/10.2140/gt.2013.17.235.

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