Jack Sonn's Home Page

Department of Mathematics, Technion

Amado 728

Tel: 04 8294180

Email: sonn@math.technion.ac.il

Algebra seminar

Research interests: algebraic number theory, Galois theory, Brauer groups of fields

Memberships:

American Mathematical Society

Israel Mathematical Union

European Mathematical Society

Graduate students:

Leonid Stern: M.Sc. 1977

Leonid Stern: Ph.D. 1982

Elias Abboud: M.Sc. 1985

Pe'erli Seter: M.Sc. 1986

Danny Kotlar: M.Sc. 1987

Hadar Porat: M.Sc. 1994

Eyal Faraggi: Ph.D. 1997

Joseph (Yossi) Cohen M.Sc. 2000

Joseph (Yossi) Cohen Ph.D. 2004

Yehonatan Sharvit M.Sc. 2005

Daniel Rabayev M.Sc. 2009

Danny Neftin Ph.D. 2011

Daniel Rabayev Ph.D. In progress

Doron Elad M.Sc. In progress

List of publications:

1. J. Sonn and H. Zassenhaus, On the theorem on the primitive element, Amer. Math. Monthly 74 (1967) 407-410

2. J. Sonn, On the embedding problem for non-solvable Galois groups of algebraic number fields: reduction theorems, Bull. Amer. Math. Soc. 58 (1972) 553-557

3. J. Sonn, On the embedding problem for non-solvable Galois groups of algebraic number fields: reduction theorems, J. Number Theory 4 (1972) 411-436

4. J. Sonn, Localizability of the embedding problem with symplectic kernel, J. Number Theory 6 (1974) 138-157

5. J. Sonn, Epimorphisms of Demushkin groups, Israel J. Math. 17 (1974) 176-190

6. J. Shapiro and J. Sonn, Free factor groups of one-relator groups, Duke Math. J. 41 (1974) 83-88

7. J. Sonn, Alternating forms and one-relator groups, AMS Proc. 46 (1974) 15-20

8. J. Sonn, Groups that are the union of finitely many subgroups, Amer. Math. Monthly 83 (1976) 263-265

9. J. Sonn, Galois groups of global fields of finite characteristic, J. Alg. 43 (1976) 606-618

10. J. Sonn, Frobenius Galois groups over quadratic fields, Israel J. Math. 31 (1978) 91-96

11. J. Sonn, Class groups and Brauer groups, Israel J. Math. 34 (1979) 97-105

12. B. Fein, M. Schacher and J. Sonn, Brauer groups of rational function fields, AMS Bull. (New Series) 1 (1979) 766-768

13. J. Sonn, SL(2,5) and Frobenius Galois groups over Q, Can. J. Math. 32 (1980) 281-293

14. J. Sonn, Rational division algebras as solvable crossed products, Israel J. Math. 37 (1980) 246-250

15. D. Chillag and J. Sonn, Sylow-metacyclic groups and Q -admissibility, Israel J. Math. 40 (1981) 307-323

16. J. Sonn, Direct summands of class groups, J. Number Theory 17 (1983) 343-349

17. J. Sonn, Q -admissibility of solvable groups, J. Algebra 84 (1983) 411-419

18. J. Sonn, Nonabelian counterexamples to the Noether problem, Proc. AMS 93 (1985) 225-226

19. J. Sonn, On equivalence of number fields, Israel J. Math. 52 (1985) 239-244

20. B. Fein, M. Schacher and J. Sonn, Brauer groups of fields of genus zero, J. Algebra 114 (1988) 479-483

21. J. Sonn, Double covers of $S_5$ and Frobenius groups as Galois groups over number fields, J. Algebra 114 (1988) 401-410

22. M. Schacher and J. Sonn, Double covers of the symmetric groups as Galois groups over number fields, J. Algebra 116 (1988) 243-250

23. J. Sonn, Double covers of alternating and symmetric groups as Galois groups over number fields, Bull. Soc. Math. Belgique 40, Ser. A (1988) 297-305

24. J. Arason, B. Fein, M. Schacher and J. Sonn, Cyclic extensions of $K(\sqrt{-1})$, Trans. AMS 313 (1989) 843-851

25. D. Kotlar, M. Schacher and J. Sonn, Central extensions of symmetric groups as Galois groups, J. Algebra 124 (1989) 183-198

26. J. Sonn, Central extensions of $S_n$ as Galois groups via trinomials, J. Algebra 125 (1989) 320-330

27. J. Sonn, Groups of small order as Galois groups over Q, Rocky Mountain J. Math. 19 (1989) 947-956

28. J. Sonn, On Brauer groups and embedding problems over function fields, J. Algebra 131 (1990) 631-640

29. J. Sonn, Central extensions of $S_n$ as Galois groups of regular extensions of Q, J. Algebra 140, no. 2 (1991) 355-359

30. M. Schacher and J. Sonn, K-admissibility of $A_6$ and $A_7$, J.Algebra 145 (1992) 333-338

31. E. Aljadeff and J. Sonn, Projective Schur division algebras are abelian crossed products, J. Algebra 163 (1994) 795-805

32. J. Sonn, Brauer groups, embedding problems, and nilpotent groups as Galois groups, Israel J. Math. 85 (1994) 391-405

33. J. Sonn, Rigidity and embedding problems over ${Bbb Q}_{ab}(t)$, J. Number Theory {\bf 47} (1994) 398-404

34. E. Aljadeff and J. Sonn, Projective Schur algebras have abelian splitting fields, J. Algebra 175 (1995) 179-187

35. S. Liedahl and J. Sonn, K-admissibility of metacyclic 2-groups, Contemp. Math. 186 (1995) 65-73

36. E. Aljadeff and J. Sonn, On the projective Schur group of a field, J. Algebra 178 (1995) 530-540

37. G. Malle and J. Sonn, Covering groups of almost simple groups as Galois groups over ${Bbb Q}_{ab}(t)$, Israel J. Math. 96 (1996) 431-444

38. E. Aljadeff and J. Sonn, Bounds on orders of finite subgroups of PGL(n,K), J. Alg. 210 (1998) 352-360

39. R. Meshulam and J. Sonn, A quantitative version of a lemma of Shafarevich-Ishkhanov, Comm. Alg. 27 (1999) 1255-1259

40. E. Aljadeff and J. Sonn, Projective Schur algebras of nilpotent type are Brauer equivalent to radical algebras, J. Alg. 220 (1999) no. 2, 401-414

41. E. Aljadeff and J. Sonn, Exponent reduction for radical abelian algebras, J. Alg. 223 (2000) 527-534

42. J. Sonn, Free pro-p groups as Galois groups over ${Bbb Q}(p)(t)$, Israel J. Math. 119 (2000) 1-8

43. E. Aljadeff and J. Sonn, Exponent reduction for projective Schur algebras, J. Alg. 239 (2001) 356-364

44. E. Aljadeff and J. Sonn, Relative Brauer groups and m-torsion, Proc. AMS 130 (2002) 1333-1337

45. J. Cohen and J. Sonn, On the Ono invariants of imaginary quadratic fields, J. Number Theory 95 (2002) 259-267

46. E. Aljadeff and J. Sonn, Fields for which the projective Schur subgroup is the whole Brauer group, Israel J. Math. 131 (2002) 375--379

47. E. Aljadeff and J. Sonn, Projective Schur groups of iterated power series fields, J. Pure Appl. Alg. 182 (2003) 109-117

48. H. Kisilevsky and J. Sonn, On the n-torsion subgroup of the Brauer group of a number field, J. Theorie des Nombres de Bordeaux, 15 (2003) 199-203

49. J. Sonn and J. Swallow, Brauer groups of genus zero extensions of number fields, Trans. AMS 357 (2005) 2723-2738

50. B. Guralnick, M. Schacher, and J. Sonn, Irreducible polynomials that are locally reducible everywhere, Proc. AMS 133 (2005) 3171--3177

51. H. Kisilevsky and J. Sonn, Abelian extensions of global fields with constant local degrees, Math. Research Letters 13, no. 4 (2006) 599-605

52. E. Aljadeff, J. Sonn and A. Wadsworth, Projective Schur groups of Henselian fields, J. Pure Applied Alg. 208 no. 3 (2007) 833-851

53. C. Popescu, J. Sonn, and A. Wadsworth, n-torsion of Brauer groups as relative Brauer groups of abelian extensions, J. Number Theory 125 (2007) 26-38

54. J. Sonn, Polynomials with roots in ${\Bbb Q}_p(t)$ for all p, Proc. AMS 136 (2008) 1955-1960.

55. J. Sonn, Two remarks on the inverse Galois problem for intersective polynomials, J. Th. Nombres de Bordeaux, 21 (2009) 437-439

56. H. Kisilevsky and J. Sonn, On the minimal ramification problem for $ell$-groups, Compositio Math. 146 (2010) 599-606

57. T. Hanke and J. Sonn, The location of noncrossed products in Brauer groups of Laurent series fields over global fields, Math. Ann. 350 (2011) 313-337

58. H. Kisilevsky, Danny Neftin, and Jack Sonn, On the minimal ramification problem for semiabelian groups, Algebra and Number Theory 4 no. 8 (2010), 1077-1090

59. D. Rabayev and J. Sonn, On Galois realizations of the 2-coverable symmetric and alternating groups, Comm. Alg. (to appear)

Preprints:

60. J. Cohen and J. Sonn, On $GCD(\Phi_N(a^n),Phi_N(b^n))$

61. Timo Hanke, Danny Neftin and Jack Sonn, Noncrossed product bounds over Henselian fields

My Technion page