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Journal articles on the topic 'Divisible group'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Sharma, Jyoti, Jagdish Prasad, and D. K. Ghosh. "Characterization of Group Divisible Designs." Mathematical Journal of Interdisciplinary Sciences 4, no. 2 (2016): 161–75. http://dx.doi.org/10.15415/mjis.2016.42014.

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2

Midha, Chand K., and Aloke Dey. "Cyclic Group Divisible Designs." Calcutta Statistical Association Bulletin 45, no. 3-4 (1995): 253–58. http://dx.doi.org/10.1177/0008068319950311.

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New cyclic solutions of several group divisible incomplete block designs arc presented, A new group divisible desian is reported whose solution is also cyclic. We also present non-isomorphic solutions of several group divisible designs listed in the catalogue of Clatworthy (1973).

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3

Rahilly, Alan. "Maximal arcs and group divisible designs." Bulletin of the Australian Mathematical Society 41, no. 2 (1990): 223–29. http://dx.doi.org/10.1017/s0004972700018037.

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The existence of maximal arcs of a certain type in symmetric designs is shown to yield semiregular group divisible designs whose duals are also semiregular group divisible. Two infinite families of such group divisible designs are constructed. The group divisible designs in these families are, in general, not symmetric.

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4

Rahilly, Alan. "Semiregular group divisible designs with dual properties." Bulletin of the Australian Mathematical Society 45, no. 1 (1992): 61–69. http://dx.doi.org/10.1017/s0004972700037011.

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A construction method for group divisible designs is employed to construct (i) infinitely many non-symmetric semiregular group divisible designs whose duals are semiregular group divisible designs, and (ii) infinitely many transversal designs whose duals are group divisible 3-associate designs. A construction method for affine α−resolvable balanced incomplete block designs is also given and illustrated.

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5

Mukerjee, Rahul, and Sanpei Kageyama. "Robustness group divisible designs." Communications in Statistics - Theory and Methods 19, no. 9 (1990): 3189–203. http://dx.doi.org/10.1080/03610929008830375.

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6

Oort, Frans. "Finite Group Schemes and $p$-Divisible Groups." Notices of the International Congress of Chinese Mathematicians 8, no. 1 (2020): 55–78. http://dx.doi.org/10.4310/iccm.2020.v8.n1.a5.

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7

Tausk, Daniel V. "A Locally Compact Non Divisible Abelian Group Whose Character Group Is Torsion Free and Divisible." Canadian Mathematical Bulletin 56, no. 1 (2013): 213–17. http://dx.doi.org/10.4153/cmb-2011-146-4.

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AbstractIt was claimed by Halmos in 1944 that if G is a Hausdorff locally compact topological abelian group and if the character group of G is torsion free, then G is divisible. We prove that such a claim is false by presenting a family of counterexamples. While other counterexamples are known, we also present a family of stronger counterexamples, showing that even if one assumes that the character group of G is both torsion free and divisible, it does not follow that G is divisible.

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8

KISHI, YASUHIRO. "ON THE IDEAL CLASS GROUP OF CERTAIN QUADRATIC FIELDS." Glasgow Mathematical Journal 52, no. 3 (2010): 575–81. http://dx.doi.org/10.1017/s0017089510000431.

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AbstractLet n(≥ 3) be an odd integer. Let k:= $\Q(\sqrt{4-3^n})\)$ be the imaginary quadratic field and k′:= $\Q(\sqrt{-3(4-3^n)})\)$ the real quadratic field. In this paper, we prove that the class number of k is divisible by 3 unconditionally, and the class number of k′ is divisible by 3 if n(≥ 9) is divisible by 3. Moreover, we prove that the 3-rank of the ideal class group of k is at least 2 if n(≥ 9) is divisible by 3.

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9

Singh, Ksh Surjit, and K. K. Singh Meitei. "Semi-Regular Group Divisible Designs For Smaller Block Size." International Journal of Innovative Research in Computer Science & Technology 6, no. 1 (2018): 6–8. http://dx.doi.org/10.21276/ijircst.2018.6.1.2.

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10

Duan, Xiaoping, and Sanpei Kageyama. "CONSTRUCTIONS OF GROUP DIVISIBLE DESIGNS." JOURNAL OF THE JAPAN STATISTICAL SOCIETY 25, no. 2 (1995): 121–28. http://dx.doi.org/10.14490/jjss1995.25.121.

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11

O'Keefe, Christine M., and Alan Rahilly. "Spreads and group divisible designs." Designs, Codes and Cryptography 3, no. 3 (1993): 229–35. http://dx.doi.org/10.1007/bf01388484.

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12

Rodger, C. A., and Julie Rogers. "Generalizing Clatworthy group divisible designs." Journal of Statistical Planning and Inference 140, no. 9 (2010): 2442–47. http://dx.doi.org/10.1016/j.jspi.2010.02.024.

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13

Heinrich, Katherine, and Jianxing Yin. "On group divisible covering designs." Discrete Mathematics 202, no. 1-3 (1999): 101–12. http://dx.doi.org/10.1016/s0012-365x(98)00362-8.

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14

Thannippara, Alex, Sreejith V, S. C. Bagui, and D. K. Ghosh. "A New Method of Construction of E-optimal Generalized Group Divisible Designs (GGDD)." Journal of Scientific Research 1, no. 1 (2008): 38–42. http://dx.doi.org/10.3329/jsr.v1i1.1697.

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In this article, we develop a new method of construction of E-optimal generalized group divisible designs through group testing designs.Â Keywords: Balanced Incomplete Block Design (BIBD); Group Divisible (GD); Generalized Group Divisible Design (GDD); E-optimality.Â Â© 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.Â DOI: 10.3329/jsr.v1i1.1697

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15

Pabhapote, Nittiya, and Narong Punnim. "Group Divisible Designs with Two Associate Classes and." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/148580.

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The original classiffcation of PBIBDs defined group divisible designs GDD() with . In this paper, we prove that the necessary conditions are suffcient for the existence of the group divisible designs with two groups of unequal sizes and block size three with .

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16

Arasu, K. T., and Alexander Pott. "Some construction of group divisible designs with singer groups." Discrete Mathematics 97, no. 1-3 (1991): 39–45. http://dx.doi.org/10.1016/0012-365x(91)90419-3.

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17

LIU, CHIA-HSIN, and D. S. PASSMAN. "MULTIPLICATIVE JORDAN DECOMPOSITION IN GROUP RINGS OF 2, 3-GROUPS." Journal of Algebra and Its Applications 09, no. 03 (2010): 483–92. http://dx.doi.org/10.1142/s0219498810004026.

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In this paper, we essentially finish the classification of those finite 2, 3-groups G having integral group rings with the multiplicative Jordan decomposition (MJD) property. If G is abelian or a Hamiltonian 2-group, then it is clear that ℤ[G] satisfies MJD. Thus, we need only consider the nonabelian case. Recall that the 2-groups with MJD were completely determined by Hales, Passi and Wilson, while the corresponding 3-groups were almost completely determined by the present authors. Thus, we are concerned here, for the most part, with groups whose order is divisible by 6. As it turns out, ther

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18

Wehrfritz, B. A. F. "The divisible radical of a group." Central European Journal of Mathematics 7, no. 3 (2009): 387–94. http://dx.doi.org/10.2478/s11533-009-0022-7.

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19

Saurabh, Shyam, and Kishore Sinha. "A new regular group divisible design." Examples and Counterexamples 1 (November 2021): 100029. http://dx.doi.org/10.1016/j.exco.2021.100029.

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20

Sastry, D. V. S. "A series of group divisible designs." Communications in Statistics - Theory and Methods 20, no. 5-6 (1991): 1677–82. http://dx.doi.org/10.1080/03610929108830591.

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21

Kageyama, Sanpei. "A construction of group divisible designs." Journal of Statistical Planning and Inference 12 (January 1985): 123–25. http://dx.doi.org/10.1016/0378-3758(85)90060-6.

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22

Arasu, K. T., and Susan Harris. "New constructions of group divisible designs." Journal of Statistical Planning and Inference 52, no. 2 (1996): 241–53. http://dx.doi.org/10.1016/0378-3758(95)00111-5.

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23

Giese, Sabine, and Ralph-Hardo Schulz. "Divisible designs with dual translation group." Designs, Codes and Cryptography 43, no. 1 (2007): 41–45. http://dx.doi.org/10.1007/s10623-007-9056-7.

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24

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

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25

Duan, Xiaoping, and Sanpei Kageyama. "Constructions of nested group divisible designs." Statistics & Probability Letters 18, no. 1 (1993): 41–48. http://dx.doi.org/10.1016/0167-7152(93)90097-3.

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26

Sinha, Kishore, and Sanpei Kageyama. "Composite construction of group divisible designs." Annals of the Institute of Statistical Mathematics 41, no. 2 (1989): 409–14. http://dx.doi.org/10.1007/bf00049405.

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27

Danchev, Peter. "Isomorphism Characterization of Divisible Groups in Modular Abelian Group Rings." gmj 16, no. 1 (2009): 49–54. http://dx.doi.org/10.1515/gmj.2009.49.

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Abstract Suppose G is an abelian group with a p-subgroup H and R is a commutative unitary ring of prime characteristic p with trivial nil-radical. We give a complete description up to isomorphism of the maximal divisible subgroups of 1 + I(RG;H) and (1 + I(RG;H))=H, respectively, where I(RG;H) denotes the relative augmentation ideal of the group algebra RG with respect to H. This paper terminates a series of works by the author on the topic, first of which are [Danchev, Rad. Mat. 13: 23–32, 2004] and [Danchev, Bull. Georgian Acad. Sci. 174: 238–242, 2006].

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28

Srivastav, Sudesh K. "ON CONSTRUCTION OF GENERALIZED GROUP DIVISIBLE DESIGNS WITH TWO GROUPS." Communications in Statistics - Theory and Methods 31, no. 4 (2002): 639–47. http://dx.doi.org/10.1081/sta-120003139.

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29

Hurd, Spencer P., and Dinesh G. Sarvate. "Group divisible designs with block size four and two groups." Discrete Mathematics 308, no. 13 (2008): 2663–73. http://dx.doi.org/10.1016/j.disc.2005.02.024.

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30

Henson, D., D. G. Sarvate, and S. P. Hurd. "Group divisible designs with three groups and block size four." Discrete Mathematics 307, no. 14 (2007): 1693–706. http://dx.doi.org/10.1016/j.disc.2006.09.017.

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31

Sarti, Alessandra. "Group Actions, Cyclic Coverings and Families of K3-Surfaces." Canadian Mathematical Bulletin 49, no. 4 (2006): 592–608. http://dx.doi.org/10.4153/cmb-2006-055-0.

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AbstractIn this paper we describe six pencils of K3-surfaces which have large Picard number (ρ = 19, 20) and each contains precisely five special fibers: four have A-D-E singularities and one is non-reduced. In particular, we characterize these surfaces as cyclic coverings of some K3-surfaces described in a recent paper by Barth and the author. In many cases, using 3-divisible sets, resp., 2-divisible sets, of rational curves and lattice theory, we describe explicitly the Picard lattices.

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32

CHOUHAN, C. P. S. "Method of Construction of Group Divisible Designs." Journal of Ultra Scientist of Physical Sciences Section A 28, no. 7 (2016): 354–57. http://dx.doi.org/10.22147/jusps-a/280703.

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33

Miao, Ying, Sanpei Kageyama, and Xiaoping Duan. "FURTHER CONSTRUCTIONS OF NESTED GROUP DIVISIBLE DESIGNS." JOURNAL OF THE JAPAN STATISTICAL SOCIETY 26, no. 2 (1996): 231–39. http://dx.doi.org/10.14490/jjss1995.26.231.

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34

Wang, Haiyan, and Yanxun Chang. "Kite-group Divisible Designs of Type gtu1." Graphs and Combinatorics 22, no. 4 (2006): 545–71. http://dx.doi.org/10.1007/s00373-006-0681-0.

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35

Tsarev, A. V. "Pseudorational rank of a quotient divisible group." Journal of Mathematical Sciences 144, no. 2 (2007): 4013–22. http://dx.doi.org/10.1007/s10958-007-0254-7.

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36

Parihar, J. S., and R. Shrivastava. "Methods of construction of group divisible designs." Journal of Statistical Planning and Inference 18, no. 3 (1988): 399–404. http://dx.doi.org/10.1016/0378-3758(88)90116-4.

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37

Fomin, A. A. "On the Quotient Divisible Group Theory. II." Journal of Mathematical Sciences 230, no. 3 (2018): 457–83. http://dx.doi.org/10.1007/s10958-018-3754-8.

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38

Assaf, Ahmed M. "An application of modified group divisible designs." Journal of Combinatorial Theory, Series A 68, no. 1 (1994): 152–68. http://dx.doi.org/10.1016/0097-3165(94)90095-7.

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39

Ji, Lijun. "Group divisible designs with large block sizes." Designs, Codes and Cryptography 86, no. 10 (2017): 2255–60. http://dx.doi.org/10.1007/s10623-017-0448-z.

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40

Fickus, Matthew, and John Jasper. "Equiangular tight frames from group divisible designs." Designs, Codes and Cryptography 87, no. 7 (2018): 1673–97. http://dx.doi.org/10.1007/s10623-018-0569-z.

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41

Larson, James R., Joseph G. Bihary, and Amanda C. Egan. "Motivation gains on divisible conjunctive group tasks." Group Processes & Intergroup Relations 21, no. 8 (2017): 1125–43. http://dx.doi.org/10.1177/1368430217702724.

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Two studies examined the effort that participants expended on a challenging physical persistence activity when that activity was a critical part of a divisible conjunctive task performed by two people working as a team compared to when it was structured as an individual task performed by one person working alone. It was found that participants put greater effort into that activity when they worked as part of a team task compared to when they worked alone—a motivation gain when working in groups. This gain occurred despite the absence of any apparent task-related ability differences among parti

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42

Brouwer, A. E., A. Schrijver, and H. Hanani. "Group divisible designs with block-size four." Discrete Mathematics 306, no. 10-11 (2006): 939–47. http://dx.doi.org/10.1016/j.disc.2006.03.015.

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43

Kharaghani, Hadi, and Sho Suda. "Linked systems of symmetric group divisible designs." Journal of Algebraic Combinatorics 47, no. 2 (2017): 319–43. http://dx.doi.org/10.1007/s10801-017-0777-z.

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44

Tamura, Hiroki. "D-optimal designs and group divisible designs." Journal of Combinatorial Designs 14, no. 6 (2006): 451–62. http://dx.doi.org/10.1002/jcd.20103.

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45

Romanovskii, N. S. "SOME issues in the theory of models of divisible rigid groups." Herald of Omsk University 28, no. 5 (2023): 10–12. http://dx.doi.org/10.24147/1812-3996.2023.5.10-12.

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A brief review of some of the author's results on the theory of models of divisible rigid groups is given. A theorem is presented that describes algebraic closures of subsets in a divisible rigid group.

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46

Girma Tefera, Zebene, and Samuel Asefa Fufa. "GDDs with 4 Groups and Block Size 5." SINET: Ethiopian Journal of Science 46, no. 2 (2023): 146–53. http://dx.doi.org/10.4314/sinet.v46i2.3.

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This paper studies a special case of group divisible designs (GDDs) called 3-GDDs, which were defined by extending the definitions of a group divisible designs and a t-design. In particular, the paper looks at a 3-GDD(n, 4, 5; μ1, μ2) with 4 groups and block size 5. Necessary conditions for the existence given.

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47

Hossein, Sahleh, and Akbar Alijani Ali. "Extensions of Locally Compact Abelian, Torsion-Free Groups by Compact Torsion Abelian Groups." British Journal of Mathematics & Computer Science 22, no. 4 (2017): 1–5. https://doi.org/10.9734/BJMCS/2017/32966.

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Let <em>X</em> be a compact torsion abelian group. In this paper, we show that an extension of <em>F<sub>p</sub></em> by <em>X</em> splits where <em>F<sub>p</sub></em> is the p-adic number group and p a prime number. Also, we show that an extension of a torsion-free, non-divisible LCA group by <em>X</em> is not split.

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48

HARASHITA, SHUSHI. "ON -DIVISIBLE GROUPS WITH SATURATED NEWTON POLYGONS." Nagoya Mathematical Journal 232 (June 7, 2017): 96–120. http://dx.doi.org/10.1017/nmj.2017.22.

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This paper concerns the classification of isogeny classes of$p$-divisible groups with saturated Newton polygons. Let$S$be a normal Noetherian scheme in positive characteristic$p$with a prime Weil divisor$D$. Let${\mathcal{X}}$be a$p$-divisible group over$S$whose geometric fibers over$S\setminus D$(resp. over$D$) have the same Newton polygon. Assume that the Newton polygon of${\mathcal{X}}_{D}$is saturated in that of${\mathcal{X}}_{S\setminus D}$. Our main result (Corollary 1.1) says that${\mathcal{X}}$is isogenous to a$p$-divisible group over$S$whose geometric fibers are all minimal. As an app

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49

SRIVASTAV, SUDESH K., and ARTI SHANKAR. "Some Methods of Constructing Generalized Group Divisible Designs with Two Groups." Communications in Statistics - Theory and Methods 34, no. 1 (2005): 127–33. http://dx.doi.org/10.1081/sta-200045854.

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50

Zhu, Mingzhi, and Gennian Ge. "Mixed group divisible designs with three groups and block size 4." Discrete Mathematics 310, no. 17-18 (2010): 2323–26. http://dx.doi.org/10.1016/j.disc.2010.05.014.

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