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Bulletin of the American Mathematical Society

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Additive group theory—A progress report


Author: Henry Mann
Journal: Bull. Amer. Math. Soc. 79 (1973), 1069-1075
MSC (1970): Primary 20F50, 05A05, 22A99
DOI: https://doi.org/10.1090/S0002-9904-1973-13341-5
MathSciNet review: 0325811
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  • 1. P. C. Baayen, Een combinatorisch probleem voor eindige Abelse groepen, Math. Centrum Syllabus 5, Colloquium Discrete Wiskunde Caput 3. Math. Centre Amsterdam, 1968. MR 249505
  • 2. Cauchy, Recherche sur les nombres, J. École Polytechn. 9 (1813), 99-106.
  • 3. I. Chowla, A theorem in the additive theory of numbers, Proc. Nat. Acad. Sci. U.S.A. 8 (1938), 160-164.
  • 4. S. Chowla, H. B. Mann and E. G. Straus, Some applications of the Cauchy-Davenport theorem, Norske Vid. Selsk. Forh. Trondheim 32 (1959), 74-80. MR 23 #A2384. MR 125077
  • 5. H. Davenport, On the addition of residue classes, J. London Math. Soc. 10 (1935), 30-32.
  • 6. H. Davenport, A historical note, J. London Math. Soc 22 (1947), 100-101. MR 9, 271. MR 22865
  • 7. P. H. Diananda and H. P. Yap, Maximal sum free sets of elements of finite groups, Proc. Japan Acad. 45 (1969), 1-5. MR 39 #6968. MR 245662
  • 8. G. T. Diderrich, An addition theorem for Abelian groups of order pq, J. Number Theory (to appear). MR 360506
  • 9. P. Erdös, A. Ginzburg and A. Ziv, Bull. Res. Council Israel 10F (1961), 41-43.
  • 10. P. Erdös and H. Heilbronn, On the addition of residue classes mod p, Acta. Arithm. 9 (1949), 149-150. MR 166186
  • 11. Boas P. van Emde, A combinatorial problem on finite Abelian groups. II, Math. Centrum Amsterdam Afd. Zuivere Wisk. 1969, ZW-007, 60 pp. MR 41 #332. MR 255672
  • 12. Boas P. van Emde and D. Kruyswijk, A combinatorial problem on finite Abelian groups. III, Math. Centrum Amsterdam Afd. Zuivere Wisk 1969 ZW-008. MR 255672
  • 13. J. H. B. Kempermann, On small sum-sets in an Abelian group, Acta. Math. 103 (1960), 63-88. MR 22 #1615. MR 110747
  • 14. J. H. B. Kempermann, On products of sets in a locally compact group, Fund. Math. 56 (1964), 51-68. MR 34 #2772. MR 202913
  • 15. M. Kneser, Abschäetzung der asymptotischen dichte von Summenmengen, Math. Z. 58 (1953), 459-484. MR 15, 104. MR 56632
  • 16. M. Kneser, Anwendung eines Satzes von Mann auf die Geometrie der Zahlen, Proc. Internat. Congress Math. Amsterdam, vol. 2, 1954, p. 32.
  • 17. M. Kneser, Ein Satz über Abelsche Gruppen mit Anwendungen auf die Geometrie der Zahlen, Math. Z. 61 (1955), 429-434. MR 16, 898. MR 68536
  • 18. M. Kneser, Summenmengen in lokal kompkaten Abelschen Gruppen, Math. Z. 66 (1956), 88-110. MR 18, 403. MR 81438
  • 19. H. B. Mann, On products of sets of group elements, Canad. J. Math. 4 (1952), 64-66. MR 13, 720. MR 46354
  • 20. H. B. Mann, An addition theorem for sets of elements of Abelian groups, Proc. Amer. Math. Soc. 4 (1953), 423. MR 14, 1058. MR 55334
  • 21. H. B. Mann, Addition theorems. The addition theorems of group theory and number theory, Interscience, New York, 1965. MR 31 #5854. MR 181626
  • 22. H. B. Mann, Two addition theorems, J. Combinatorial Theory 3 (1967), 233-235. MR 36 #1349. MR 218262
  • 23. H. B. Mann and J. E. Olson, Sums of sets of elements in the elementary Abelian group of type (p, p), J. Combinatorial Theory 2 (1967), 275-284. MR 35 #5506. MR 214657
  • 24. William A. McWorter, On a theorem of Mann, Amer. Math. Monthly 71 (1964), 285-286. MR 28 #5135. MR 161931
  • 25. John E. Olson, An addition theorem modulo p, J. Combinatorial Theory 5 (1968), 45-52. MR 37 #2714. MR 227129
  • 26. John E. Olson, A combinatorial problem on finite Abelian groups. I, J. Number Theory 1 (1969), 8-10. MR 38 #5922. MR 237641
  • 27. John E. Olson, A combinatorial problem on finite Abelian groups. II, J. Number Theory 1 (1969), 195-199. MR 39 #1552. MR 240200
  • 28. A. H. Rhemtulla and A. P. Street, Maximal sum free sets in finite Abelian groups, Bull. Austral. Math. Soc. 2 (1970), 289-297. MR 41 #8519. MR 263920
  • 29. A. Tietäväinen, On diagonal forms over a finite field, Ann. Univ. Turku. Ser. AI No. 118 (1968), 1-10. MR 38 #3248. MR 234934
  • 30. A. G. Vosper, The critical pairs of subsets of a group of prime order, J. London Math. Soc. 31 (1956), 200-205. MR 17, 1056. MR 77555
  • 31. A. G. Vosper, Addendum to "The critical pairs of subsets of a group of prime order", J. London Math. Soc. 31 (1956), 280-282. MR 17, 1182. MR 78368
  • 32. Y. F. Wou, Sums of sets in the Abelian group of type (5, 5), J. Number Theory (to appear). MR 399034
  • 33. H. P. Yap, Maximal sum free sets of group elements, J. London Math. Soc. 44 (1969), 131-136. MR 38 #1167. MR 232844
  • 34. H. P. Yap, Maximal sum free sets in finite Abelian groups. II, Bull. Austral. Math. Soc. 5 (1971), 43-54. MR 45 #3564. MR 294494

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DOI: https://doi.org/10.1090/S0002-9904-1973-13341-5

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