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Journal articles on the topic 'Dihedral groups'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 April 2022

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1

El-Sanfaz, Mustafa Anis, Nor Haniza Sarmin, and Siti Norziahidayu Amzee Zamri. "Generalized Commuting Graph of Dihedral, Semi-dihedral and Quasi-dihedral Groups." Malaysian Journal of Fundamental and Applied Sciences 17, no. 6 (December 31, 2021): 711–19. http://dx.doi.org/10.11113/mjfas.v17n6.2245.

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Commuting graphs are characterized by vertices that are non-central elements of a group where two vertices are adjacent when they commute. In this paper, the concept of commuting graph is extended by defining the generalized commuting graph. Furthermore, the generalized commuting graph of the dihedral groups, the quasi-dihedral groups and the semi-dihedral groups are presented and discussed. The graph properties including chromatic and clique numbers are also explored.

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2

Sehrawat, Sudesh, and Manju Pruthi. "Codes over dihedral groups." Journal of Information and Optimization Sciences 39, no. 4 (May 19, 2018): 889–901. http://dx.doi.org/10.1080/02522667.2017.1406628.

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3

Bowler, Andrew. "Orthomorphisms of dihedral groups." Discrete Mathematics 167-168 (April 1997): 141–44. http://dx.doi.org/10.1016/s0012-365x(96)00222-1.

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4

Guyot, Luc. "Limits of dihedral groups." Geometriae Dedicata 147, no. 1 (December 11, 2009): 159–71. http://dx.doi.org/10.1007/s10711-009-9447-1.

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5

Isbell, John. "Sequencing certain dihedral groups." Discrete Mathematics 85, no. 3 (December 1990): 323–28. http://dx.doi.org/10.1016/0012-365x(90)90389-y.

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6

Blagojević, Dragan. "Unions of dihedral groups." Semigroup Forum 33, no. 1 (December 1986): 293–98. http://dx.doi.org/10.1007/bf02573205.

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7

Eliahou, Shalom, and Michel Kervaire. "Sumsets in dihedral groups." European Journal of Combinatorics 27, no. 4 (May 2006): 617–28. http://dx.doi.org/10.1016/j.ejc.2003.09.023.

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8

Etayo Gordejuela, José Javier, and Ernesto Martínez. "The real genus of cyclic by dihedral and dihedral by dihedral groups." Journal of Algebra 296, no. 1 (February 2006): 145–56. http://dx.doi.org/10.1016/j.jalgebra.2005.03.038.

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9

Celentani, Maria Rosaria, Antonella Leone, and Chiara Nicotera. "Infinite locally dihedral groups as automorphism groups." Ricerche di Matematica 63, S1 (August 8, 2014): 69–73. http://dx.doi.org/10.1007/s11587-014-0201-0.

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10

Baumeister, Barbara, Christian Haase, Benjamin Nill, and Andreas Paffenholz. "Polytopes associated to dihedral groups." Ars Mathematica Contemporanea 7, no. 1 (January 8, 2013): 30–38. http://dx.doi.org/10.26493/1855-3974.289.91d.

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11

Erdmann, K. "Algebras and Dihedral Defect Groups." Proceedings of the London Mathematical Society s3-54, no. 1 (January 1987): 88–114. http://dx.doi.org/10.1112/plms/s3-54.1.88.

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12

Crans, Alissa S., Thomas M. Fiore, and Ramon Satyendra. "Musical Actions of Dihedral Groups." American Mathematical Monthly 116, no. 6 (June 2009): 479–95. http://dx.doi.org/10.1080/00029890.2009.11920965.

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13

Li, Paul. "Sequencing the dihedral groups D4k." Discrete Mathematics 175, no. 1-3 (October 1997): 271–76. http://dx.doi.org/10.1016/s0012-365x(96)00108-2.

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14

Ueberberg, Johannes. "Projective planes and dihedral groups." Discrete Mathematics 174, no. 1-3 (September 1997): 337–45. http://dx.doi.org/10.1016/s0012-365x(97)80336-6.

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15

Chebolu, Sunil K., and Keir Lockridge. "Fuchs' problem for dihedral groups." Journal of Pure and Applied Algebra 221, no. 4 (April 2017): 971–82. http://dx.doi.org/10.1016/j.jpaa.2016.08.015.

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16

Crans, Alissa S., Thomas M. Fiore, and Ramon Satyendra. "Musical Actions of Dihedral Groups." American Mathematical Monthly 116, no. 6 (June 1, 2009): 479–95. http://dx.doi.org/10.4169/193009709x470399.

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17

Płonka, Ernest. "Symmetric Words in Dihedral Groups." Algebra Colloquium 17, spec01 (December 2010): 953–62. http://dx.doi.org/10.1142/s1005386710000891.

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Let G be a group and let w = w(x1, x2,…, xn) be a word in the absolutely free group Fn on free variables x1, x2,…, xn. The set S(n)(G) of all words w such that the equality w(gσ1, gσ2,…, gσn) = w(g1, g2,…, gn) holds for all g1, g2,…, gn∈G and all permutations σ ∈ Sn is a subgroup of Fn, called the subgroup of n-symmetric words for G. In this paper, the groups S(2)(Dp) and S(3)(Dp) for dihedral groups Dp are determined, where p > 3 is a prime. In particular, it turns out that the groups S(3)(Dp) are not abelian.

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18

Leung, Ka Hin, Siu Lun Ma, and Yan Loi Wong. "Difference sets in dihedral groups." Designs, Codes and Cryptography 1, no. 4 (December 1991): 333–38. http://dx.doi.org/10.1007/bf00124608.

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19

Lemmermeyer, Franz. "Class groups of dihedral extensions." Mathematische Nachrichten 278, no. 6 (May 2005): 679–91. http://dx.doi.org/10.1002/mana.200310263.

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20

Płonka, Ernest. "Weak automorphisms of dihedral groups." Algebra universalis 64, no. 1-2 (October 2010): 153–60. http://dx.doi.org/10.1007/s00012-010-0096-x.

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21

McCollum, Joseph. "Random Walks on Dihedral Groups." Journal of Theoretical Probability 24, no. 2 (September 10, 2010): 397–408. http://dx.doi.org/10.1007/s10959-010-0307-6.

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22

Kuhn, Heinrich. "A dihedral calculus for groups." Archiv der Mathematik 51, no. 2 (August 1988): 111–17. http://dx.doi.org/10.1007/bf01206467.

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23

Berenstein, Arkady, and Michael Kapovich. "Affine buildings for dihedral groups." Geometriae Dedicata 156, no. 1 (April 19, 2011): 171–207. http://dx.doi.org/10.1007/s10711-011-9598-8.

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24

Achar, P. N., and A. M. Aubert. "Springer Correspondences for Dihedral Groups." Transformation Groups 13, no. 1 (March 2008): 1–24. http://dx.doi.org/10.1007/s00031-008-9004-2.

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25

Evans, J. D. P. "Syzygy modules for dihedral groups." Communications in Algebra 49, no. 6 (February 15, 2021): 2606–22. http://dx.doi.org/10.1080/00927872.2021.1879106.

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26

Izquierdo, M. "On Klein Surfaces and Dihedral Groups." MATHEMATICA SCANDINAVICA 76 (December 1, 1995): 221. http://dx.doi.org/10.7146/math.scand.a-12538.

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27

Ecker, Jürgen. "Affine Completeness of Generalised Dihedral Groups." Canadian Mathematical Bulletin 49, no. 3 (September 1, 2006): 347–57. http://dx.doi.org/10.4153/cmb-2006-035-8.

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AbstractIn this paper we study affine completeness of generalised dihedral groups. We give a formula for the number of unary compatible functions on these groups, and we characterise for every k ∈ N the k-affine complete generalised dihedral groups. We find that the direct product of a 1-affine complete group with itself need not be 1-affine complete. Finally, we give an example of a nonabelian solvable affine complete group. For nilpotent groups we find a strong necessary condition for 2-affine completeness.

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28

Hubbard, David. "Dihedral side extensions and class groups." Journal of Number Theory 128, no. 4 (April 2008): 731–37. http://dx.doi.org/10.1016/j.jnt.2007.04.008.

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29

Chen, Jin-Quan, Peng-Dong Fan, Luke McAven, and Philip Butler. "Algebraic solutions for all dihedral groups." Journal of Mathematical Physics 41, no. 12 (December 2000): 8196–222. http://dx.doi.org/10.1063/1.1286513.

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30

Hidalgo, Rubén A. "Dihedral groups are of schottky type." Proyecciones (Antofagasta) 18, no. 1 (July 1999): 23–48. http://dx.doi.org/10.22199/s07160917.1999.0001.00003.

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31

Lu, Lu, Qiongxiang Huang, and Xueyi Huang. "Integral Cayley graphs over dihedral groups." Journal of Algebraic Combinatorics 47, no. 4 (August 31, 2017): 585–601. http://dx.doi.org/10.1007/s10801-017-0787-x.

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32

Laubenbacher, Reinhard C., and Bruce A. Magurn. "Sk2 and K3 Of Dihedral Groups." Canadian Journal of Mathematics 44, no. 3 (June 1, 1992): 591–623. http://dx.doi.org/10.4153/cjm-1992-037-x.

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AbstractNew computations of birelative K2 groups and recent results on K3 of rings of algebraic integers are combined in generalized Mayer-Vietoris sequences for algebraic k-theory. Upper and lower bounds for SK2(ℤ G) and lower bounds for K3(ℤ G) are deduced for G a dihedral group of square-free order, and for some other closely related groups G.

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33

Kakkar, Vipul, and Gopal Singh Rawat. "Commuting graphs of generalized dihedral groups." Discrete Mathematics, Algorithms and Applications 11, no. 02 (April 2019): 1950024. http://dx.doi.org/10.1142/s1793830919500241.

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For a group [Formula: see text] and a subset [Formula: see text] of [Formula: see text], the commuting graph of [Formula: see text], denoted by [Formula: see text] is the graph whose vertex set is [Formula: see text] and any two vertices [Formula: see text] and [Formula: see text] in [Formula: see text] are adjacent if and only if they commute in [Formula: see text]. In this paper, certain properties of the commuting graph of generalized dihedral groups have been studied.

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34

DeWolf, Darien, Charles Edmunds, and Christopher Levy. "On commutation semigroups of dihedral groups." Semigroup Forum 87, no. 2 (April 10, 2013): 467–88. http://dx.doi.org/10.1007/s00233-013-9483-x.

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35

Kovács, István, and Young Soo Kwon. "Regular Cayley maps for dihedral groups." Journal of Combinatorial Theory, Series B 148 (May 2021): 84–124. http://dx.doi.org/10.1016/j.jctb.2020.12.002.

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36

Xu, Yuan. "Intertwining Operators Associated with Dihedral Groups." Constructive Approximation 52, no. 3 (November 15, 2019): 395–422. http://dx.doi.org/10.1007/s00365-019-09487-w.

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37

Li, Zheng Xing, and Yuan Lin Li. "Coleman automorphisms of generalized dihedral groups." Acta Mathematica Sinica, English Series 32, no. 2 (January 15, 2016): 251–57. http://dx.doi.org/10.1007/s10114-016-5228-6.

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38

Deleaval, L., N. Demni, and H. Youssfi. "Dunkl kernel associated with dihedral groups." Journal of Mathematical Analysis and Applications 432, no. 2 (December 2015): 928–44. http://dx.doi.org/10.1016/j.jmaa.2015.07.029.

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39

B�lek, Martin, Ale? Dr�pal, and Natalia Zhukavets. "The Neighbourhood of Dihedral 2-Groups." Acta Applicandae Mathematicae 85, no. 1-3 (January 2005): 25–33. http://dx.doi.org/10.1007/s10440-004-5582-8.

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40

Chen, Huey Voon, and Chang Seng Sin. "On complete decompositions of dihedral groups." ITM Web of Conferences 36 (2021): 03001. http://dx.doi.org/10.1051/itmconf/20213603001.

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Let G be a finite non-abelian group and B1, …, Bt be nonempty subsets of G for integer t ≥ 2. Suppose that B1, …, Bt are pairwise disjoint, then (B1, …, Bt) is called a complete decomposition of G of order t if the subset product Bi1 … Bit = {bi1 … bit | bij ∈ Bij, j = 1,2, …,t} coincides with G, where {Bi1 … Bit} = {B1, …, Bt} and the Bij are all distinct. Let D2n = ‹r,s| rn = s2 = 1, rs =srn-1› be the dihedral group of order 2n for integer n ≥3. In this paper, we shall give the constructions of the complete decompositions of D2n of order t, where 2 ≤ t ≤ n.

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41

Umar, Abdullahi, and Bashir Ali. "Dihedral Groups as Epimorphic Images of Some Fibonacci Groups." Sultan Qaboos University Journal for Science [SQUJS] 18 (December 1, 2013): 54. http://dx.doi.org/10.24200/squjs.vol18iss0pp54-59.

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The Fibonacci groups are deﬁned by the presentation where , and all subscripts are assumed to be reduced modulo . In this paper we give an alternative proof that for , , and are all inﬁnite by establishing a morphism (or group homomorphism) onto the dihedral group for all .

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42

Muranov, Yu V. "Tate cohomologies and Browder-Livesay groups of dihedral groups." Mathematical Notes 54, no. 2 (August 1993): 798–805. http://dx.doi.org/10.1007/bf01212844.

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43

Brown, Kenneth A. "Class groups and automorphism groups of group rings." Glasgow Mathematical Journal 28, no. 1 (January 1986): 79–86. http://dx.doi.org/10.1017/s0017089500006376.

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This paper is a sequel to [2]. A polycyclic-by-finite group G was there called dihedral free if G contains no subgroup isomorphic to 〈b, a:ba = b-1 a2 = 1〉 whose normalizer has finite index in G. It was shown in [2, Theorem F] that, if R is a commutative Noetherian domain, the group ring RG is a prime Noetherian maximal order if and only if R is integrally closed, G is dihedral free, and G has no non-trivial finite normal subgroups. Throughout, R and G will be assumed to satisfy these hypotheses. The main aim of the paper is to study the class group of the maximal order RG.

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44

Niemenmaa, Markku. "On loops which have dihedral 2-groups as inner mapping groups." Bulletin of the Australian Mathematical Society 52, no. 1 (August 1995): 153–60. http://dx.doi.org/10.1017/s0004972700014520.

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In this paper we consider the situation that a group G has a subgroup H which is a dihedral 2-group and with connected transversals A and B in G. We show that G is then solvable and moreover, if G is generated by the set A ∪ B, then H is subnormal in G. We apply these results to loop theory and it follows that if the inner mapping group of a loop Q is a dihedral 2-group then Q is centrally nilpotent.

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45

Wang, Na-Er, Kan Hu, Kai Yuan, and Jun-Yang Zhang. "Smooth skew morphisms of the dihedral groups." Ars Mathematica Contemporanea 16, no. 2 (March 28, 2019): 527–47. http://dx.doi.org/10.26493/1855-3974.1475.3d3.

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46

Poimenidou, Eirini, and Amy Cottrell. "Total Characters of Dihedral Groups and Sharpness." Missouri Journal of Mathematical Sciences 12, no. 1 (February 2000): 12–25. http://dx.doi.org/10.35834/2000/1201012.

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47

Cho, Eung. "s-Smith equivalent representations of dihedral groups." Pacific Journal of Mathematics 135, no. 1 (November 1, 1988): 17–28. http://dx.doi.org/10.2140/pjm.1988.135.17.

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48

Staneková, L'ubica. "t-Balanced Cayley maps of dihedral groups." Electronic Notes in Discrete Mathematics 28 (March 2007): 301–7. http://dx.doi.org/10.1016/j.endm.2007.01.043.

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49

Bleher, Frauke M. "Universal deformation rings and dihedral defect groups." Transactions of the American Mathematical Society 361, no. 07 (July 1, 2009): 3661. http://dx.doi.org/10.1090/s0002-9947-09-04543-7.

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50

Kohl, Timothy. "Multiple Holomorphs of Dihedral and Quaternionic Groups." Communications in Algebra 43, no. 10 (July 6, 2015): 4290–304. http://dx.doi.org/10.1080/00927872.2014.943842.

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