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Journal articles on the topic 'Group theory – Mathematics'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Huetinck, Linda. "Group Theory: It's a SNAP." Mathematics Teacher 89, no. 4 (April 1996): 342–46. http://dx.doi.org/10.5951/mt.89.4.0342.

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Martin Gardner has compared the concept of a mathematical group to the grin of the Cheshue Cat. “The body of the cat (algebra as traditionally taught) vanishes, leaving only an abstract grin. A grin implies something amusing. Perhaps we can make group theory less mysterious if we do not take it too seriously” (Gardner 1966). A game like “It's a SNAP” can be used to introduce mathematical groups and make them appear less mysterious. This mathematics manipulative allows students to play with the concepts of group theory and develop an understanding of modern algebra.

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2

Stonehewer, Stewart. "MATHEMATICAL WORKS I: GROUP THEORY." Bulletin of the London Mathematical Society 28, no. 2 (March 1996): 219–20. http://dx.doi.org/10.1112/blms/28.2.219.

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3

Pride, Stephen J. "CONTRIBUTIONS TO GROUP THEORY (Contemporary Mathematics, 33)." Bulletin of the London Mathematical Society 17, no. 6 (November 1985): 610–12. http://dx.doi.org/10.1112/blms/17.6.610.

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4

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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5

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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6

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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7

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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8

Steingart, Alma. "A group theory of group theory: Collaborative mathematics and the ‘uninvention’ of a 1000-page proof." Social Studies of Science 42, no. 2 (February 23, 2012): 185–213. http://dx.doi.org/10.1177/0306312712436547.

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9

Streater, R. F. "APPLICATIONS OF GROUP THEORY IN PHYSICS AND MATHEMATICAL PHYSICS (Lectures in Applied Mathematics 21)." Bulletin of the London Mathematical Society 19, no. 5 (September 1987): 500. http://dx.doi.org/10.1112/blms/19.5.500a.

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10

Beardon, Alan F. "Complex Exponents and Group Theory." Mathematics Magazine 93, no. 3 (May 20, 2020): 186–92. http://dx.doi.org/10.1080/0025570x.2020.1736876.

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11

Moore, Vardeman G. "Recursive functions in group theory." Illinois Journal of Mathematics 30, no. 2 (June 1986): 284–94. http://dx.doi.org/10.1215/ijm/1256044637.

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12

Allhebi, Bayan Khaled. "PROBABILISTIC STRATEGIES IN GROUP THEORY." Far East Journal of Mathematical Sciences (FJMS) 123, no. 2 (April 20, 2020): 181–208. http://dx.doi.org/10.17654/ms123020181.

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13

Salce, Luigi. "Abelian Group Theory in Italy." Rocky Mountain Journal of Mathematics 32, no. 4 (December 2002): 1229–43. http://dx.doi.org/10.1216/rmjm/1181070019.

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14

Makhnev, A. A. "School-conferences on group theory." Proceedings of the Steklov Institute of Mathematics 267, S1 (December 2009): 244–47. http://dx.doi.org/10.1134/s0081543809070220.

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15

Elliott, George A., Toshikazu Natsume, and Ryszard Nest. "The Heisenberg group andK-theory." K-Theory 7, no. 5 (September 1993): 409–28. http://dx.doi.org/10.1007/bf00961535.

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16

Humphreys, J. E. "Book Review: Group theory and physics." Bulletin of the American Mathematical Society 32, no. 4 (October 1, 1995): 455–58. http://dx.doi.org/10.1090/s0273-0979-1995-00612-9.

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17

Murphy, G. J., and L. Tuset. "Aspects of compact quantum group theory." Proceedings of the American Mathematical Society 132, no. 10 (June 2, 2004): 3055–67. http://dx.doi.org/10.1090/s0002-9939-04-07400-3.

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18

Eklof, Paul C. "The Affinity of Set Theory and Abelian Group Theory." Rocky Mountain Journal of Mathematics 32, no. 4 (December 2002): 1119–34. http://dx.doi.org/10.1216/rmjm/1181070012.

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19

Artamonov, V. A., and A. A. Bovdi. "Integral group rings: Groups of units and classical K-theory." Journal of Soviet Mathematics 57, no. 2 (November 1991): 2931–58. http://dx.doi.org/10.1007/bf01099283.

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20

Alexanderson, Gerald L., and Brian Hayes. "Group Theory in the Bedroom." College Mathematics Journal 37, no. 4 (September 1, 2006): 322. http://dx.doi.org/10.2307/27646368.

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21

Wang, Xiao Gang. "Significance of Mathematization of Philosophical Problems from the Angle of Broadspectrum Philosophy." Advanced Materials Research 433-440 (January 2012): 6315–18. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.6315.

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Whether philosophy can realize mathematization has long been controversial. As the mathematics develops a nonquantative branch- structural mathematics, however, mathematization of philosophy has a turnaround. Broadspectrum philosophy which makes use of structural mathematics has established a generally applicable as well as precise mathematical model for many philosophical problems, giving a positive answer to whether the philosophy can be mathematized. Mathematizaiton of philosophy allows more accurate and clear distinction of people’s expression in meaning, gives ideas the visible characteristics, makes philosophy an analyzable discipline, and realizes routinization of philosophical methods. Hegel was well versed in mathematics but opposed “Extreme Mathematic Attitude”, since he thought recognizing all the objects from the mathematic standpoint of “Quantity or Quantitative Relationship” would ignore the qualitative difference among the objects.［1］P239 Hegel’s opinion was based on the traditional mathematic which takes the Quantitative Relationship as the foundation. Holding the same evidence as Hegel's, most philosophers nowadays still suspect that the philosophy can be mathematized. When the modern mathematics has developed a new nonquantative branch, the Structural Mathematics, the philosophy mathematization, however, meets a turning point. Opposed to Quantitative Mathematics, the Structural Mathematics focuses on research of mathematic relationship and structure on the basis of abstract set theory. Since the structural mathematics doesn't rely on quantity and quantitative relationship, it can be combined in research of philosophy which usually doesn’t possess quantitative characteristics. Establishment of Broadspectrum Philosophy is a successful attempt. With full application of set theory, symbolic logic, modern algebra, transformation group theory and graph theory, Broadspectrum Philosophy constructs a generally applicable as well as precise mathematical mode for many philosophical problems, bringing a fundamental change to the philosophy. This paper attempts to make some preliminary analysis on the significance of establishment of Broadspectrum Philosophy.

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22

Lynch, Mark A. M. "Generating quasigroups: a group theory investigation." International Journal of Mathematical Education in Science and Technology 42, no. 6 (September 15, 2011): 806–12. http://dx.doi.org/10.1080/0020739x.2011.562318.

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23

Auslander, L., and R. Tolimieri. "Radar Ambiguity Functions and Group Theory." SIAM Journal on Mathematical Analysis 16, no. 3 (May 1985): 577–601. http://dx.doi.org/10.1137/0516043.

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24

Webb, David L. "G-theory of group rings for groups of square-free order." K-Theory 1, no. 4 (July 1987): 417–22. http://dx.doi.org/10.1007/bf00539626.

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25

Kuku, Aderemi O., and Guoping Tang. "Higher K -theory of group-rings of virtually infinite cyclic groups." Mathematische Annalen 325, no. 4 (April 1, 2003): 711–26. http://dx.doi.org/10.1007/s00208-002-0397-2.

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26

Garimella, Ramesh. "A Counter Example in Group Theory." Missouri Journal of Mathematical Sciences 3, no. 2 (May 1991): 77–78. http://dx.doi.org/10.35834/1991/0302077.

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27

Chen, Quan-Guo, Yang-Lei Pang, and Ding-Guo Wang. "Galois theory for comatrix group corings." Studia Scientiarum Mathematicarum Hungarica 55, no. 3 (September 2018): 281–92. http://dx.doi.org/10.1556/012.2018.55.3.1399.

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28

Neumann, Peter M. "GROUP THEORY: essays for Philip Hall." Bulletin of the London Mathematical Society 18, no. 3 (May 1986): 311. http://dx.doi.org/10.1112/blms/18.3.311.

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29

Neumann, Peter M. "Two Combinatorial Problems in Group Theory." Bulletin of the London Mathematical Society 21, no. 5 (September 1989): 456–58. http://dx.doi.org/10.1112/blms/21.5.456.

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30

Dunwoody, M. J. "COMBINATORIAL GROUP THEORY: A TOPOLOGICAL APPROACH." Bulletin of the London Mathematical Society 24, no. 2 (March 1992): 191–92. http://dx.doi.org/10.1112/blms/24.2.191.

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31

Goppa, V. D. "Group representations and algebraic information theory." Izvestiya: Mathematics 59, no. 6 (December 31, 1995): 1123–47. http://dx.doi.org/10.1070/im1995v059n06abeh000051.

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32

Ren, Yunxiang. "Universal skein theory for group actions." Advances in Mathematics 356 (November 2019): 106804. http://dx.doi.org/10.1016/j.aim.2019.106804.

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33

Lesh, Kathryn. "Infinite loop spaces from group theory." Mathematische Zeitschrift 225, no. 3 (July 16, 1997): 467–83. http://dx.doi.org/10.1007/pl00004622.

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34

Léandre, Rémi. "Positivity theorem in semi-group theory." Mathematische Zeitschrift 258, no. 4 (June 23, 2007): 893–914. http://dx.doi.org/10.1007/s00209-007-0204-6.

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35

Toledo, Domingo. "Book Review: Geometric group theory, Vol. 2: Asymptotic invariants of infinite groups." Bulletin of the American Mathematical Society 33, no. 03 (July 1, 1996): 395–99. http://dx.doi.org/10.1090/s0273-0979-96-00669-6.

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36

Moretó, A. "Some problems in number theory that arise from group theory." Publicacions Matemàtiques EXTRA (June 1, 2007): 181–91. http://dx.doi.org/10.5565/publmat_pjtn05_09.

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37

Brauer, R. "Book Review: The theory of group representations." Bulletin of the American Mathematical Society 37, no. 01 (December 21, 1999): 100——100. http://dx.doi.org/10.1090/s0273-0979-99-00823-x.

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38

Ralph, William J. "Category and group rings in homotopy theory." Transactions of the American Mathematical Society 299, no. 1 (January 1, 1987): 205. http://dx.doi.org/10.1090/s0002-9947-1987-0869408-2.

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39

Martina, L. "Exotic Galileian group in field theory." Journal of Mathematical Sciences 136, no. 6 (August 2006): 4465–69. http://dx.doi.org/10.1007/s10958-006-0237-0.

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40

Vavilov, N. A., V. I. Mysovskikh, and Yu G. Teterin. "Computational group theory in St. Petersburg." Journal of Mathematical Sciences 95, no. 2 (June 1999): 2070–73. http://dx.doi.org/10.1007/bf02169961.

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41

Fomin, A. A. "To Quotient Divisible Group Theory. I." Journal of Mathematical Sciences 197, no. 5 (February 20, 2014): 688–97. http://dx.doi.org/10.1007/s10958-014-1752-z.

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42

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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43

Melhuish, Kathleen. "Three Conceptual Replication Studies in Group Theory." Journal for Research in Mathematics Education 49, no. 1 (January 2018): 9–38. http://dx.doi.org/10.5951/jresematheduc.49.1.0009.

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Many studies in mathematics education research occur with a nonrepresentative sample and are never replicated. To challenge this paradigm, I designed a large-scale study evaluating student conceptions in group theory that surveyed a national, representative sample of students. By replicating questions previously used to build theory around student understanding of subgroups, cyclic groups, and isomorphism with over 800 students, I establish the utility of replication studies to (a) validate previous results, (b) establish the prevalence of various student conceptions, and (c) reexamine theoretical propositions. Data analyzed include 1 round of open-ended surveys, 2 rounds of closed-form surveys, and 30 follow-up interviews. I illustrate the potential of replication studies to refine theory and theoretical propositions in 3 ways: by offering alternate interpretations of student responses, by challenging previous pedagogical implications, and by reevaluating connections between theories

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44

Holton, Derek, and John Wenzel. "A student‐centred approach to group theory." International Journal of Mathematical Education in Science and Technology 24, no. 6 (November 1993): 883–88. http://dx.doi.org/10.1080/0020739930240613.

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45

Afgani, Muhammad Win, Didi Suryadi, and Jarnawi Afgani Dahlan. "The enhancement of pre-service mathematics teachers’ mathematical understanding ability through ACE teaching cyclic." Journal of Technology and Science Education 9, no. 2 (March 1, 2019): 153. http://dx.doi.org/10.3926/jotse.441.

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The aim of this study was to investigate the enhancement of the mathematical understanding ability of pre-service mathematics teachers through Activity-Class Discussion-Exercise (ACE) teaching cyclic based on APOS theory. This study used a quasi-experiment method with non-equivalent pre-post test control group design. The subjects of this study were 120 pre-service mathematics teachers from two universities in Palembang, Indonesia. The subjects were divided into two class, that is, experiment and control class. Experiment class was a class that is applied ADE teaching cyclic based on APOS theory, whereas control class was a class that is applied direct learning. The subjects were also divided into three groups of mathematical initial ability, that is, high, average, and low. The Instruments used in this study were mathematical initial ability test, mathematical understanding ability test, observation, and interview. Data analysis tests used in this study were statistic test of parametric and non-parametric. The results of data analysis showed that 1) there is no significant difference between the improvement of mathematical understanding ability of pre-service mathematics teachers applied ACE teaching cyclic based on APOS theory and direct learning in terms of overall and the group of mathematical initial ability, 2) there is no interaction between learning factors (APOS and direct learning) and the group of mathematical initial ability (high, average, and low) to the improvement of mathematical understanding ability of pre-service mathematics teachers.

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46

Sela, Z. "Diophantine geometry over groups VII: The elementary theory of a hyperbolic group." Proceedings of the London Mathematical Society 99, no. 1 (February 23, 2009): 217–73. http://dx.doi.org/10.1112/plms/pdn052.

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47

Pramasdyahsari, A. S., R. D. Setyawati, and I. U. Albab. "How group theory and school mathematics are connected: an identification of mathematics in-service teachers." Journal of Physics: Conference Series 1663 (October 2020): 012068. http://dx.doi.org/10.1088/1742-6596/1663/1/012068.

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48

Satoh, Takao. "On the low-dimensional cohomology groups of the IA-automorphism group of the free group of rank three." Proceedings of the Edinburgh Mathematical Society 64, no. 2 (May 2021): 338–63. http://dx.doi.org/10.1017/s0013091521000171.

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AbstractIn this paper, we study the structure of the rational cohomology groups of the IA-automorphism group $\mathrm {IA}_3$ of the free group of rank three by using combinatorial group theory and representation theory. In particular, we detect a nontrivial irreducible component in the second cohomology group of $\mathrm {IA}_3$, which is not contained in the image of the cup product map of the first cohomology groups. We also show that the triple cup product of the first cohomology groups is trivial. As a corollary, we obtain that the fourth term of the lower central series of $\mathrm {IA}_3$ has finite index in that of the Andreadakis–Johnson filtration of $\mathrm {IA}_3$.

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49

Le, Maohua. "A Dibisibility I Problem Concerning Group Theory." Pure and Applied Mathematics Quarterly 8, no. 3 (2012): 689–92. http://dx.doi.org/10.4310/pamq.2012.v8.n3.a5.

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50

Feldman, Arnold D. "Constructing a Minimal Counterexample in Group Theory." Mathematics Magazine 58, no. 1 (January 1, 1985): 24. http://dx.doi.org/10.2307/2690233.

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