Some interactions between group theory and the general theory of algebras

  • Ralph McKenzie
Surveys
First Online:
Part of the Lecture Notes in Mathematics book series (LNM, volume 1456)

Keywords

Normal Subgroup Finite Group Sylow Subgroup Universal Algebra Congruence Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Belkin, V. P., ‘Quasi-identities of finite rings and lattices’, Algebra i Logika 17 (1978), 247–259.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Birkhoff, G., ‘On the combination of subalgebras’, Proc. Cambridge Philos. Soc. 29 (1933), 441–464.CrossRefMATHGoogle Scholar
  3. [3]
    Birkhoff, G., ‘On the structure of abstract algebras’, Proc. Cambridge Philos. Soc. 31 (1935), 433–454.CrossRefMATHGoogle Scholar
  4. [4]
    Birkhoff, G., Lattice Theory, Third Edition, Colloquium Publications 25 (Amer. Math. Soc., Providence, 1967).MATHGoogle Scholar
  5. [5]
    Bryant, R. M., ‘The laws of finite pointed groups’, Bull. London Math. Soc. 14 (1982), 119–123.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    Burris, S., Sankappanavar, H. P., A Course in Universal Algebra, Graduate Texts in Mathematics 78 (Springer-Verlag, New York, 1981).MATHGoogle Scholar
  7. [7]
    Chang, C. C., Jónsson, B., Tarski, A., ‘Refinement properties for relational structures’, Fund. Math. 55 (1964), 249–281.MathSciNetMATHGoogle Scholar
  8. [8]
    Cohn, P. M., Universal Algebra, Revised Edition (D. Reidel Publ. Co., Boston Dordrecht London, 1981).CrossRefMATHGoogle Scholar
  9. [9]
    Crawley, P., Dilworth, R. P., Algebraic Theory of Lattices (Prentice-Hall, Englewood Cliffs, 1973).MATHGoogle Scholar
  10. [10]
    Freese, R., ‘Free modular lattices’, Trans. Amer. Math. Soc. 261 (1980), 81–91.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Freese, R., McKenzie, R., ‘Residually small varieties with modular congruence lattices’, Trans. Amer. Math. Soc. 264 (1981), 419–430.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    Freese, R., McKenzie, R., Commutator Theory for Congruence Modular Varieties, London Math. Soc. Lecture Note Ser. 125 (Cambridge University Press, Cambridge, 1987).MATHGoogle Scholar
  13. [13]
    Golubov, E. A., Sapir, M. V., ‘Varieties of finitely approximable semigroups’, Soviet Math. Dokl. 20 (1979), 828–832.MathSciNetMATHGoogle Scholar
  14. [14]
    Grätzer, G., General Lattice Theory (Academic Press, New York, 1978).CrossRefMATHGoogle Scholar
  15. [15]
    Grätzer, G., Universal Algebra, Second Edition (Springer-Verlag, New York, 1979).MATHGoogle Scholar
  16. [16]
    Gross, H., Herrmann, C., Moresi, R., ‘The classification of subspaces in Hermitean vector spaces’, J. Algebra 105 (1987), 516–541.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    Hagemann, J., Herrmann, C., ‘A concrete ideal multiplication for algebraic systems and its relation to congruence-distributivity’, Arch. Math. (Basel) 32 (1979), 234–245.MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    Herrmann, C., ‘On the word problem for the modular lattice with four free generators’, Math. Ann. 256 (1983), 513–527.MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    Hobby, D., McKenzie, R., The Structure of Finite Algebras, Contemporary Math. 76 (Amer. Math. Soc., Providence, 1988).MATHGoogle Scholar
  20. [20]
    Kurosh, A. G., Lectures on General Algebra (Chelsea Publ. Co., New York, 1965).MATHGoogle Scholar
  21. [21]
    Lampe, W., ‘A property of lattices of equational theories’, Algebra Universalis 23 (1986), 61–69.MathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    Mal’cev, A. I., Algebraic Systems (Springer-Verlag, New York, 1973).CrossRefGoogle Scholar
  23. [23]
    McKenzie, R., ‘On finite groupoids and K-prime algebras’, Trans. Amer. Math. Soc. 133 (1968), 115–129.MathSciNetMATHGoogle Scholar
  24. [24]
    McKenzie, R., ‘Cardinal multiplication of structures with a reflexive relation’, Fund. Math. 70 (1971), 59–101.MathSciNetMATHGoogle Scholar
  25. [25]
    McKenzie, R., ‘Residually small varieties of semigroups’, Algebra Universalis 13 (1981), 171–201.MathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    McKenzie, R., ‘Narrowness implies uniformity’, Algebra Universalis 15 (1982a), 67–85.MathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    McKenzie, R., ‘Residually small varieties of K-algebras’, Algebra Universalis 14 (1982b), 181–196.MathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    McKenzie, R., ‘A note on residually small varieties of semigroups’, Algebra Universalis 17 (1983), 143–149.MathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    McKenzie, R. N., McNulty, G. F., Taylor, W. F., Algebras, Lattices, Varieties, vol. I (Wadsworth and Brooks/Cole, Monterey, California, 1987).MATHGoogle Scholar
  30. [30]
    McKenzie, R., Valeriote, M., The Structure of Decidable Locally Finite Varieties, Progress in Math. 79 (Birkhauser, Boston, 1989).CrossRefMATHGoogle Scholar
  31. [31]
    McNulty, G., Shallon, C., ‘Inherently nonfinitely based finite algebras’, in Universal Algebra and Lattice Theory, ed. by R. Freese and O. Garcia, Lecture Notes in Math. 1004, pp. 205–231 (Springer-Verlag, Berlin, 1983).CrossRefGoogle Scholar
  32. [32]
    Ol’shanskii, A. Yu., ‘Varieties of finitely approximable groups’, Math. USSR—Izv. 3 (1969), 867–877 (1971).MATHGoogle Scholar
  33. [33]
    Ol’shanskii, A. Yu., ‘Conditional identities in finite groups’, Siber. Math. J. 15 (1974), 1000–1003 (1975).MathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    Pálfy, P. P., Pudlák, P., ‘Congruence lattices of finite algebras and intervals in subgroup lattices of finite groups’, Algebra Universalis 11 (1980), 22–27.MathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    Pigozzi, D., ‘Finite basis theorems for relatively congruence-distributive quasivarieties’, Proc. Amer. Math. Soc. (to appear).Google Scholar
  36. [36]
    Power, S. C., ‘Infinite tensor products of upper triangular matrix algebras’, Math. Scand. (1989) (to appear).Google Scholar
  37. [37]
    Power, S. C., ‘Classifications of tensor products of operator algebras’ (preprint).Google Scholar
  38. [38]
    Sapir, M. V., ‘Problems of Burnside type and the finite basis property in varieties of semigroups’, Math. USSR—Izv. 30 (1988a), 295–314.MathSciNetGoogle Scholar
  39. [39]
    Sapir, M. V., ‘Inherently nonfinitely based finite semigroups’, Math. USSR—Sb. 61 (1988b), 155–166.MathSciNetMATHGoogle Scholar
  40. [40]
    Sapir, M. V., Shevrin, L. N., ‘Residually small varieties of groups and semigroups’, Izv. Vyssh. Uchebn. Zaved. Mat. (1988), No.10 (317), 41–49.Google Scholar
  41. [41]
    Smith, J. D. H., Mal’cev Varieties, Lecture Notes in Math. 554 (Springer-Verlag, Berlin, 1976).CrossRefMATHGoogle Scholar
  42. [42]
    Taylor, W., ‘Residually small varieties’, Algebra Universalis 2 (1972), 33–53.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Ralph McKenzie
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of MathematicsLa Trobe UniversityBundooraAustralia

Personalised recommendations