Publications
of Robert Guralnick

1.

Subfields of algebraically closed fields (with M. Miller), Math. Mag. 50 (1977), 260-261.

2.

On cyclic commutator subgroups (with B. Gordon and M. Miller), Aequationes Math. 17 (1978), 241-248.

3.

On decomposable commutator subgroups, Glasgow Math. J. 19 (1978), 159-162.

4.

A remark concerning unipotent matrix groups (with O. Taussky), Linear and Multilinear Algebra 7 (1979), 87-89.

5.

A note on pairs of matrices with rank one commutator, Linear and Multilinear Algebra 8 (1979), 97-99.

6.

On a result of Schur, J. Algebra 59 (1979), 302-309.

7.

Maximal subfields of algebraically closed fields (with M. Miller), J. Austral. Math. Soc. (A) 29 (1980), 462-468.

8.

A note on the local global principle for similarity of matrices, Lin. Algebra App. 30 (1980), 241-245.

9.

Expressing group elements as commutators, Rocky Mountain Math. J. 10 (1980), 651-654.

10.

On cyclic commutator subgroups, Aequationes Math. 21(1980), 33-38.

11.

Triangularization of sets of matrices, Linear and Multilinear Algebra 9 (1980), 133-140.

12.

Nonexistence of partial traces on nonsolvable groups (with I.M. Issacs and D.S. Passman), Rocky Mountain Math. J. 11 (1981), 235-245.

13.

Roth's theorems and decomposition of modules, Lin. Algebra Appl. 39 (1981), 156-165.

14.

Similarity of matrices over local rings, Lin. Algebra Appl. 41 (1981), 161-174.

15.

Isomorphism of modules under ground ring extension, J. Number Theory 14 (1982), 307-314.

16.

Generation of the lower central series, Glasgow Math. J. 23 (1982), 15-20.

17.

Commutators and commutator subgroups, Advances in Math. 45 (1982), 319-330.

18.

Module equivalences: Local to global when primitive polynomials represent units (with D. Estes), J. Algebra 77 (1982), 138-157.

19.

Matrix equivalence and isomorphism of modules, Lin. Algebra Appl. 43 (1982), 125-136.

20.

Solvable generation of groups and Sylow subgroups of the lower central series (with M. Aschbacher), J. Algebra 77 (1982), 189-201.

21.

An identity of Schur, Linear and Multilinear Algebra 12 (1983), 281-284.

22.

Pseudosimilarity and cancellation of modules (with C. Lanski), Lin. Algebra Appl. 47 (1982), 111-115.

23.

Subgroups of prime power index in a simple group, J. Algebra 81 (1983), 304-311.

24.

Subgroups inducing the same permutation representation, J. Algebra 81 (1983), 312-319.

25.

The rank of a commutator (with C. Lanski), Linear and Multilinear Algebra 13(1983), 167-175.

26.

Relative Brauer groups of global fields (with B. Fein and M. Schacher), Archiv Der Math. 41 (1983), 309-318.

27.

The genus of a module, J. Number Theory 18 (1984), 169-177.

28.

Some applications of the first cohomology group (with M. Aschbacher), J. Algebra 90 (1984), 446-460.

29.

Generation of the lower central series II, Glasgow Math. J. 25 (1984), 193-201.

30.

Equations of prime powers (with D. Estes, M. Schacher, and E. Straus), Pacific J. Math. 118 (1985), 359-367.

31.

Representations under ring extensions: Latimer-MacDuffee and Taussky correspondences (with D. Estes), Advances in Math. 54 (1984), 302-313.

32.

Lifting homomorphisms of modules, Illinois J. Math. 29 (1985), 153-156.

33.

Invariants of finite linear groups on relatively free algebras, Linear Alg. and Appl. 72 (1985), 85-92.

34.

Subgroups inducing the same permutation representation II (with D. Wales), J. Algebra 96 (1985), 94-113.

35.

Two generator groups III (with J.L. Brenner and J. Wiegold), in Contemp. Math. 33 (1984), 82-88.

36.

Power cancellation of modules, Pacific J. Math 124 (1986), 131-144.

37.

Roth's theorems for sets of matrices, Linear Alg. and Appl. 71 (1985), 113-117.

38.

Modules under ground ring extension, p. 150-156 in Order and their Applications edited by I. Reiner and K. Roggenkamp, Lecture Notes in Mathematics, vol. 1142, Springer Verlag, New York, 1984.

39.

Generation of simple groups, J. Algebra 103 (1986), 381-401.

40.

The genus of a module II: Roiter's theorem, power cancellation and extension of scalars, J. Number Theory 26 (1987), 149-165.

41.

Projective modules with free multiples and powers (with H. Bass), Proc. AMS 96 (1986), 207-208.

42.

Polynomial rings over Goldie rings are often Goldie (with V. Camillo), Proc. AMS 98 (1986), 567-568.

43.

The dimension of the first cohomology group, p.94 - 97 in Representation Theory II Groups and Orders, edited by V. Dlab, P. Gabriel and G. Michler. Lecture Notes in Mathematics Vol. 1178, Springer Verlag New York, 1985.

44.

Torsion in the Picard group and extension of scalars (with H. Bass), J. Pure Applied Algebra 52 (1988), 213-217.

45.

Matrices and representations over rings of analytic functions and other one dimensional rings, Mathematics Series, Texas Tech University. Visiting Scholars Lectures 1986-1987, 15 (1988), 15-35.

46.

Similarity of holomorphic matrices, Linear Algebra & Appl. 99 (1988), 85-96.

47.

Presentation of modules when ideals need not be principal (with L. Levy), Illinois J. Math. 32 (1988), 593-653.

48.

Elementary divisor theorem for noncommutative domains (with L. Levy and C. Odenthal), Proc. Amer. Math. Soc. 104 (1988), 1003-1011.

49.

Finite groups of genus zero (with J. G. Thompson), J. Algebra 131 (1990), 303-341.

50.

On the number of generators of a finite group, Archiv. der Math. 53 (1989), 521-523.

51.

Zeroes of permutation characters with applications to prime splitting and Brauer groups, J. Algebra 131 (1990), 294-302.

52.

On abelian quotients of primitive permutation groups (with M. Aschbacher), Proc. AMS 107 (1989), 89-95.

53.

Normalizing elements of the trace ring of generic matrices (with S. Montgomery), Comm. Algebra 17 (1989), 1805-1813.

54.

Cancellation counterexamples in Krull dimension 1 (with L. Levy and R. Warfield), Proc. AMS 109 (1990), 323-326.

55.

Cancellation and direct summands in dimension 1 (with L. Levy), J. Algebra 141 (1991), 310 - 347.

56.

Galois groups and the multiplicative structure of field extensions (with R. Wiegand), Trans. AMS 331 (1992), 563-584.

57.

A question of Stafford about affine PI algebras, Comm. Alg. 18 (1990), 3055-3057.

58.

On the cohomology of alternating and symmetric groups and decomposition of relation modules (with W. Kimmerle), J. Pure and Applied Algebra 69 (1990), 135-140.

59.

Primitive permutation characters (with J. Saxl), Groups, Combinatorics and Geometry, M. Liebeck and J. Saxl, Ed., LMS LNS 165, Cambridge Univ. Press, Cambridge, 1992, 364-367.

60.

The genus of a permutation group, Groups, Combinatorics and Geometry, M. Liebeck and J. Saxl, Ed., LMS LNS 165, Cambridge Univ. Press, Cambridge, 1992, 351-363.

61.

On invertible bimodules and automorphisms of noncommutative rings (with S. Montgomery), Trans. AMS, 341 (1994), 917-937.

62.

A note on commuting pairs of matrices, Linear and Multilinear Algebra 31 (1992), 71-75.

63.

Similarity of matrices over commutative rings, Linear Algebra and its Applications 157 (1991), 55-68.

64.

Sylow p-subgroups and subnormal subgroups of finite groups (with P. Kleidman and R. Lyons), Proc. London Math. Soc., 66 (1993), 129-151.

65.

A remark on infinite torsion groups with periodic cohomology (with O. Talelli), Comm. in Algebra 20 (1992), 1217-1221.

66.

Bimodules over pi rings, Methods in Module Theory, G. Abrams, J. Haefner, K. Rangaswama, Eds., Marcel Dekker, 1992, 117-134.

67.

Solitary Galois extensions of algebraic number fields (with L. Stern), J. Number Theory 50 (1995), 1-32.

68.

Eigenvalues of symmetric matrices and graphs (with H. Bass and D. Estes), J. Algebra, 168 (1994), 536-567.

69.

Probability of generating a classical group, (with W. Kantor and J. Saxl), Communications in Algebra, 22 (1994), 1395-1402.

70.

On extensions of the Baer-Suzuki theoreom (with G. Robinson), Israel J. Math., 82 (1993), 281-297.

71.

Transitive permutation lattices in the same genus and embeddings of subgroups (with A. Weiss), Contemp. Math., 153 (1993), 21-33.

72.

Matrices over differential fields which commute with their derivative (with W. Adkins and J. C. Evard), Lin. Algebra. & Appl., 190 (1993), 253-261.

73.

Schur covers and the Carlitz conjecture (with M. Fried. and J. Saxl), Israel J. Math, 82 (1993), 157-225.

74.

Minimal polynomials of integral symmetric matrices (with D. Estes), Lin. Algebra. & Appl., 192 (1993), 83-99.

75.

Invertible preservers and algebraic groups, Lin. Algebra. & Appl. 212/213 (1994), 249-257.

76.

Multiplicative groups of fields modulo the product of subfields (with J.-L. Colliot-Thélène and R. Wiegand), Journal Pure and Appl. Algebra 106 (1996), 233-262.

77.

Picard groups, cancellation, and the multiplicative structure of fields (with R. Wiegand), Zero-dimensional commutative rings (Knoxville, TN, 1994), 65-79, Lecture Notes in Pure and Appl. Math., 171, Dekker, New York, 1995.

78.

On the Picard group: torsion and the kernel induced by a faithfully flat map (with D. Jaffe, W. Raskind and R. Wiegand), J. Algebra 183 (1996), 420-455.

79.

Normalizing elements in PI rings (with C. Robson and L. Small), Proc. Amer. Math. Soc. 123 (1995), 1955-1957.

80.

Monodromy groups of polynomials (with J. Saxl) in Groups of Lie type and their Geometries, DiMartino and Kantor,eds, Cambridge University Press, 1995, 125-150.

81.

Monodromy groups of branched coverings: the generic case (with M. Neubauer), in Recent developments in the inverse Galois problem (Seattle, WA, 1993), 325-352, Contemp. Math. 186, Amer. Math. Soc., Providence, RI, 1995.

82.

Invertible preservers and algebraic groups II: preservers of similarity invariants and overgroups of PSL_n(F), Linear and Mult. Algebra 43 (1997), 221-255.

83.

Invertible preservers and algebraic groups III (with C. K. Li), Linear and Mult. Algebra, 43 (1997), 257 - 282.

84.

Bounds for fixed point free elements in a transitive group and applications to curves over finite fields (with D. Wan), Israel J. Math 101 (1997), 255-287.

85.

A stable range for quadratic forms over commutative rings (with D. Estes), J. Pure and Applied Algebra 120 (1997), 255-280.

86.

Permutability of characters on algebras (with L. Grunenfelder, T. Kosir, H. Radjavi), Pacific J. Math. 178 (1997), 63-70.

87.

The Picard group of a certain pullback domain: a non-commutative approach (with R. Wiegand), Commutative ring theory (Fès, 1995), 339-347, Lecture Notes in Pure and Appl. Math., 185, Dekker, New York, 1997.

88.

Modules for algebraic groups with finitely many orbits on subspaces (with M. Liebeck, D. Macpherson, G. Seitz), J. Algebra 196 (1997), 211-250.

89.

Exceptional polynomials of affine type (with P. Müller), J. Algebra 194 (1997), 429-454.

90.

On the minimal degree of a permutation representation (with K. Maagard), J. Algebra, 207 (1998), 127-145.

91.

Shirshov's theorem and representations of semigroups (with A. Freedman, R. Gupta), Pacific J. Math. 178 (1997), 63-70.

92.

Linear group with orders having certain large prime divisors (with C. Praeger, T. Pentilla and J. Saxl), Proc. London Math. Soc., to appear.

93.

Probabilistic generation of simple groups (with W. Kantor), J. Algebra, to appear.

94.

The first cohomology group and generation of simple groups (with C. Hoffman), Proceedings of a Conference on Groups and Geometry, Siena, Trends in Mathematics, 81-90, Birkäuser Verlag, 1998.

95.

Genus class groups and separable base change (with R. Wiegand) in Factorization in integral domains, 333-347, Lecture Notes in Pure and Appl. Math., 189, Dekker, New York, 1997.

96.

Low dimensional representations of special linear groups in cross characteristics (with P. Tiep), J. London Math. Soc. 78 (1999), 116 - 138.

97.

Some applications of subgroup structure to probabilistic generation and covers of curves, Proceedings of NATO Algebraic Groups Conference, Cambridge, Kluwer, 1998.

98.

Small dimensional representations are semisimple, J. Algebra, to appear.

99.

Probabilistic generation of simple groups (with M. Liebeck, A. Shalev, J. Saxl), J. Algebra, to appear.

100.

On p-singular Elements in Chevalley Groups in Characteristic p (with Frank Lübeck), preprint.

101.

Generation of simple groups by conjugates (with J. Saxl), preprint.

102.

The rational function analogue of a question of Schur and exceptionality of permutation representations, (with P. Müller, J. Saxl), preprint.

103.

Small dimensional representations of odd sympletic groups in cross characteristic (with K. Magaard and J. Saxl), preprint.

104.

Polynomials with prescribed monodromy (with M. Zieve), preprint.

105.

Cyclic quotients of transitive subgroups and extension of constants, preprint.

106.

Torsion in the genus class groups (with C. Pappacena), Proceedings of Conference in honor of Hyman Bass, submitted.