Jack Sonn's Home Page

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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

Daniel Rabayev  M.Sc.  2009

Danny Neftin   Ph.D.  2011

Daniel Rabayev  Ph.D. 2013

Doron Elad  M.Sc. 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 (2010),  Math. Ann. (online)

 

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

 

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 Hanke, Danny Neftin and Jack Sonn,  Noncrossed product bounds over Henselian fields,  Algebra and Number theory (to appear)

 

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