Jack Sonn's Home Page

HPIM1364.jpg

Department of Mathematics, Technion

Amado 728

Tel: 04 8294180

Email: sonn@math.technion.ac.il

 

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

Danny Neftin Ph.D. 2011

Daniel Rabayev M.Sc. 2009

Daniel Rabayev Ph.D. 2013

 

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, Number 2 (2011) 313-337

(appears in arXiv as Noncrossed products in Witts theorem)

 

58. Hershy Kisilevsky, Danny Neftin, and Jack Sonn, On the minimal ramification problem for semiabelian groups, Algebra and Number Theory 4 (2010), No. 8, 10771090

 

59.  Daniel Rabayev and Jack Sonn, On Galois realizations of the 2-coverable symmetric and alternating groups Comm. Alg. 42 no. 1 (2014) 253-258

 

60.  Timo HankeDanny Neftin and Jack Sonn Noncrossed product bounds over Henselian fields Algebra and Number theory 8 (2014)  837-855

 

61.  Joseph Cohen and Jack  Sonn A cyclotomic generalization of the sequence GCD(a^n-1,b^n-1) J. Th. Nombres de Bordeaux 27 (2015)  53-65

 

62.  Vsevolod Lev and Jack Sonn, Quadratic residues and difference sets modulo p Quart. J. Math. Oxford  (2016)

 

63.  Daniela Bubboloni and Jack Sonn Intersective $S_n$ polynomials with few irreducible factors, Manuscripta Math. 151 no. 3 (2016) 477-492 

 

 

 

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