Prof. Dr. Bernhard Amberg

 

University address

Institut für Mathematik,
Johannes Gutenberg-Universität Mainz,          
D-55099  Mainz, Germany.
fon:  + 49 - 6131 - 392 0284
fax:  + 49 - 6131 - 392 0915
e-mail: Amberg@uni-mainz.de     


Home address

Michael-Müller-Ring 29,
D-55128  Mainz, Germany.
fon:  + 49 - 6131 - 338306
fax:  + 49 - 6131 - 368345
e-mail: Bernhard.Amberg@t-online.de

 Amberg.jpg

 

My Students

 

Publications

 A. Research Articles

  1. Products of locally cyclic groups, Arch. Math. 117 (2021), 19-28  (with Ya. P. Sysak).
  2. Products of groups which contain abelian subgroups of small index,  J. Group Theory 20 (2017), 1061-1072   (with Ya. P. Sysak).
  3. Groups factorized by pairwise permutable abelian subgroups of finite rank,  Advances in Group Theory and Applications 2 (2016), 13-24  (with Ya. P. Sysak).
  4. On products of groups which contain abelian subgroups of index at most 2,  J. Group Theory 16 (2013), 299–318  (with Ya. P. Sysak).
  5. On the soluble graph of a finite simple group, Comm. Algebra 41 (2013)  p. 2297–2309  (with L. S. Kazarin).
  6. ABA-groups with cyclic subgroup B,  Trudy Inst. Mat. i Mekh. UrO RAN 18(3) (2012), 10--22  (with L. S. Kazarin).
  7. Large subgroups of a finite group of even order, Proc. AMS 140 (2012), 69--82  (with L. S. Kazarin).
  8. Products of locally dihedral subgroups, J. Algebra 350 (2012), 308--317  (with A. Fransman and L. S. Kazarin).
  9. Periodic groups saturated by dihedral subgroups, in: Ischia Group Theory 2010, World Scientific, Singapore (2011), 11-19  (with L. S. Kazarin).
  10. On the product of two Chernikov subgroups, Israel J. Math. 175 (2010), 363--389  (with L. S. Kazarin).
  11. Trifactorized locally finite groups with min-p for every prime p, Arch. Math. 92 (2009), 558--565  (with A. Fransman and L. S. Kazarin).
  12. Products of two groups containing cyclic subgroups of index at most 2, Arch. Math. 90 (2008), 101--111  (with Ya. P. Sysak).
  13. On the poduct of a nilpotent group and a group with non-trivial center, J. Algebra 311 (2007), 69-95  (with L. S. Kazarin).
  14. A solubility criterion for finite groups, Arch. Math.  85 (2005), 9--14  (with L. S. Kazarin).
  15. Criteria for the solubility and non-simplicity of finite groups, J. Algebra 285 (2005), 58--72  (with A. Carocca and L. S. Kazarin).
  16. Semilocal rings with n-Engel multiplicative group, Arch. Math. 83 (2004), 416-421  (with Ya. P. Sysak).
  17. Associative rings with metabelian adjoint group, J. Algebra 277 (2004), 456-473  (with Ya. P. Sysak).
  18. Local nearrings with dihedral multiplicative group, J. Algebra 273 (2004), 700-717  (with P. Hubert and Ya. P. Sysak).
  19. On the powers of a commutative nilpotent algebra, Advances in Algebra, 1-12, World Sci. Publishing, River Edge, NJ, USA (2003)  (with L. S. Kazarin).
  20. On the central series of the adjoint group of a nilpotent p-algebra, Publ. Math. Debrecen 63 (2003), 473-482  (with L. S. Kazarin).
  21. On associative rings with locally nilpotent adjoint semigroup,  Comm. Algebra 31 (2003), 123-132  (with Ya. P. Sysak).
  22. Radical rings with soluble adjoint group, J. Algebra 247 (2002), 692-702  (with Ya. P. Sysak).
  23. On minimal nilpotent algebras of a given nilpotency class, Proc. Steklov Inst. Math., Suppl. 2 (2001), S16-S25  (with L. S. Kazarin). 
  24. Commutative nilpotent p-algebras with small dimension, in: M. Curzio - F. de Giovanni (eds), Topics in Infinite Groups, Quaderni di Mat. 8 (2001), 1-20  (with L. S.Kazarin).
  25. On the dimension of a nilpotent algebra, Mat. Zametki (Mathematical Notes) 70 (2001), 483-490  (with L. S. Kazarin).
  26. Associative rings whose adjoint semigroup is locally nilpotent, Arch. Math. 76 (2001), 426-435  (with Ya. P. Sysak).
  27. Radical rings with Engel conditions, J. Algebra 231 (2000), 364-373  (with Ya. P. Sysak).
  28. The dimension of nilpotent 2-algebras with two generators, Proc. Gomel State University 3(16) Problems in Algebra (2000), 76-79  (with L. S. Kazarin).
  29. On the adjoint group of a finite nilpotent p-algebra, J. Math. Sci. 102 (2000), 3979-3997  (with L. S. Kazarin).
  30. Radical modules over group algebras of groups with finite p-rank, Preprint Series of our Department, 13 (1999)  (with Ya. P. Sysak).
  31. On groups with a locally nilpotent triple factorization II, Proceedings "Groups - Korea '97", De Gruyter, Berlin (1999), 7-18  (with Ya. P. Sysak).
  32. On the rank of a product of two finite p-groups and nilpotent p-algebra, Comm. Algebra 27 (8) (1999), 3895-3907  (with L. S. Kazarin).
  33. Konechnye gruppy s kratnymi faktorizaciyami (Finite groups with multiple factorizations), Fundamentalnaya i prikladnaya matematika 4 (1999), 1251-1263  (with B. Höfling and L. S. Kazarin).
  34. Subgroups of the adjoint group of a radical ring , Can. J. Math., 50 (1998), 3-15  (with O. Dickenschied and Ya. P. Sysak).
  35. On finite products of soluble groups, Israel J. Math. 106 (1989), 93-108  (with L. S. Kazarin).
  36. On groups with a locally nilpotent triple factorization, Publ. Math. Debrecen 50/1-2 (1996), 1-7  (with Ya. P. Sysak).
  37. Locally soluble products of two subgroups with finite rank, Comm. Algebra 24(7) (1996), 2421-2445  (with Ya. P. Sysak).
  38. Locally soluble products of minimax groups, Proceedings "Groups - Korea '94", Eds.: Kim/Johnson, DeGruyter, Berlin (1995), (1995), 9-14  (with Ya. P. Sysak).
  39. On the rank of a finite product of two p-groups, Proceedings "Groups - Korea '94", Eds.: Kim/Johnson, DeGruyter, Berlin (1995), 1-8  (with L. S. Kazarin).
  40. Groups with finite torsion-free rank which have a locally nilpotent triple factorization, J. Algebra 178 (1995), 136-148  (with Ya. P. Sysak).
  41. On the adjoint group of a radical ring, Can. Math. Bull. 38 (1995), 262-270  (with O. Dickenschied).
  42. FC-nilpotent products of hypercentral groups, Forum Math. 7 (1995), 307-316  (with S. Franciosi and F. de Giovanni).
  43. On finite products of nilpotent groups, Arch. Math. 63 (1994), 1-8  (with B. Höfling).
  44. Products of groups and group classes, Israel J. Math. 87 (1994), 9-18  (with A. Fransman).
  45. Rank formulae for factorized groups, Ukrain. Math. J. 43 (1991), 1078-1084  (with S. Franciosi and F. de Giovanni).
  46. Triply factorized groups, Comm. Algebra 18 (1990), 789-809  (with S. Franciosi and F. de Giovanni).
  47. Groups with a triple factorization, Ricerche Mat. 37 (1989), 51-62  (with N. Halbritter).
  48. Nilpotent-by-noetherian factorized groups, Can. Math. Bull. 32 (1989), 391-403  (with S. Franciosi and F. de Giovanni).
  49. On trifactorized soluble minimax groups, Arch. Math. 51 (1988), 13-19  (with S. Franciosi and F. de Giovanni).
  50. Groups with a supersoluble triple factorization, J. Algebra 177 (1988), 136-148  (with S. Franciosi and F. de Giovanni).
  51. Groups with a nilpotent triple factorization, Bull. Austral. Math. Soc. 37 (1988), 69-79  (with S. Franciosi and F. de Giovanni).
  52. On normal subgroups of products of nilpotent groups, J. Austral. Math. Soc. (Series A) 44 (1988), 275-286  (with S. Franciosi and F. de Giovanni).
  53. Groups with an FC-nilpotent triple factorization, Ricerche Mat. 36 (1987), 103-114  (with S. Franciosi and F. de Giovanni).
  54. Products of groups with finite rank, Arch. Math. 49 (1987), 369-375.
  55. Products of locally finite groups with min-p, J. Austral. Math. Soc. (Series A) 41 (1986), 352-360  (with R. Moghaddam).
  56. Produkte von Gruppen mit endlichem torsionsfreiem Rang, Arch. Math. 45 (1985), 398-406.
  57. On groups which are the product of abelian subgroups, Glasgow Math. J. 26 (1985), 151-156.
  58. Soluble groups which are products of nilpotent minimax groups, Arch. Math. 42 (1984), 385-390  (with D. J. S. Robinson).
  59. Factorized groups with max, min and min-p, Bull. Can. Math. Soc. 27 (1984), 171-178.
  60. Products of two abelian subgroups, Rocky Mountain J. Math. 14 (1984), 541-547.
  61. Über den Satz von Kegel und Wielandt, Arch. Math. 40 (1983), 289-296.
  62. Soluble products of two locally finite groups with min-p for every prime p, Rend. Sem. Mat. Univ. Padova 69 (1983), 7-17.
  63. Lokal endlich-auflösbare Produkte von zwei hyperzentralen Gruppen, Arch. Math. 35 (1980), 228-238.
  64. Über auflösbare Produkte nilpotenter Gruppen, Arch. Math. 30 (1978), 361-363.
  65. Factorizations of infinite soluble groups, Rocky Mountain J. Math. 7 (1977), 1-17.
  66. Artinian and noetherian factorized groups, Rend. Sem. Mat. Univ. Padova 55 (1976), 105-122.
  67. Factorizations of infinite groups, Habilitationsschrift, Universität Mainz, 1973.
  68. Extensions of group theoretical properties, Ill. J. Math. 16 (1972), 11-25.
  69. Abelian factorizations of infinite groups, Math. Z. 123 (1971), 201-214.
  70. On groups with chain conditions, Can. J. Math. 23 (1971), 151-159.
  71. Products of abelian groups, Proc. Amer. Math. Soc. 26 (1970), 541-547  (with W. R. Scott).
  72. Groups with maximum conditions, Pac. J. Math. 38 (1970), 9-19.
  73. Gruppentheoretische Eigenschaften und Normalisatorbedingungen, Rend. Sem. Mat. Univ. Padova 41 (1968), 97-118.
  74. Gruppen mit Minimalbedingung für Subnormalteiler, Arch. Math. 19 (1968), 348-358.
  75. Noethersche Gruppen mit Normalisatorbedingung, Arch. Math. 19 (1968), 265-278.
  76. Fastpolyminimaxgruppen, Math. Ann. 175 (1968), 44-49.

B. Survey Articles  

  1. Products of groups which contain abelian subgroups of finite index,  Note Mat. 34 (2014), 23-33.
  2. Factorization of groups and related topics, Science in China Series A: Mathematics 52, Springer-Verlag (2009), 217-230  (with L. S. Kazarin).
  3. Nilpotent p-algebras and factorized p-groups, Proceedings of "Groups St. Andrews 2005" , London Math. Society Lecture Note Series 339, Vol 1, Cambridge Univ. Press (2007), 130-147 (with L. S. Kazarin).
  4. Radical rings and their adjoint groups, in: M. Curzio - F. de Giovanni (eds), Topics in Infinite Groups, Quaderni di Mat. 8 (2001), 21-44  (with Ya. P. Sysak).
  5. Radical rings and their adjoint groups, In: Papers in Group Theory, Doerk's 60th  birthday in Calpe, Valencia (1999).
  6. Radical rings and products of groups, In: Groups - Bath 1997, Vol. I, Eds.: Campbell/Robertson/Ruskuc/Smith, London Math. Soc. Lecture Note Series 260, Cambridge University Press (1998), 1-19  (with Ya. P. Sysak).
  7. Products of groups and radical rings, First Jamaican Conference on Group Theory, Kingston, Jamaica (1996).
  8. Some results and problems about factorized groups, In: Infinite groups 94, Eds.: de Giovanni/Newell, DeGruyter, Berlin (1995), 1-22.
  9. Triply factorized groups, In: Groups - St.Andrews 1989, Eds.: Campbell/ Robertson, London Math. Soc. Lecture Note Series 159, Cambridge University Press (1990), 1-13.
  10. Infinite factorized groups, In: Groups - Korea 1988, Eds.: Kim/Neumann, Lecture Notes in Mathematics 1398, Springer, Berlin (1988), 1-24.
  11. Infinite factorized groups: Results and problems, In: Workshop on Algebra and Number Theory, Pusan, Korea (1987).
  12. Soluble groups which are the product of a nilpotent and a polycyclic subgroup, In: Proceedings of the Singapore Group Theory Conference 1987, Eds.: Cheng et al., DeGruyter, Berlin (1988)  (with S. Franciosi and F. de Giovanni).

C. Books  

  1. Products of Groups, Oxford Mathematical Monographs, Clarendon Press, Oxford (1992), 220 p.  (with S. Franciosi and F. de Giovanni).