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Some interactions between group theory and the general theory of algebras

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References

  1. Belkin, V. P., ‘Quasi-identities of finite rings and lattices’, Algebra i Logika 17 (1978), 247–259.

    Article  MathSciNet  MATH  Google Scholar 

  2. Birkhoff, G., ‘On the combination of subalgebras’, Proc. Cambridge Philos. Soc. 29 (1933), 441–464.

    Article  MATH  Google Scholar 

  3. Birkhoff, G., ‘On the structure of abstract algebras’, Proc. Cambridge Philos. Soc. 31 (1935), 433–454.

    Article  MATH  Google Scholar 

  4. Birkhoff, G., Lattice Theory, Third Edition, Colloquium Publications 25 (Amer. Math. Soc., Providence, 1967).

    MATH  Google Scholar 

  5. Bryant, R. M., ‘The laws of finite pointed groups’, Bull. London Math. Soc. 14 (1982), 119–123.

    Article  MathSciNet  MATH  Google Scholar 

  6. Burris, S., Sankappanavar, H. P., A Course in Universal Algebra, Graduate Texts in Mathematics 78 (Springer-Verlag, New York, 1981).

    MATH  Google Scholar 

  7. Chang, C. C., Jónsson, B., Tarski, A., ‘Refinement properties for relational structures’, Fund. Math. 55 (1964), 249–281.

    MathSciNet  MATH  Google Scholar 

  8. Cohn, P. M., Universal Algebra, Revised Edition (D. Reidel Publ. Co., Boston Dordrecht London, 1981).

    Book  MATH  Google Scholar 

  9. Crawley, P., Dilworth, R. P., Algebraic Theory of Lattices (Prentice-Hall, Englewood Cliffs, 1973).

    MATH  Google Scholar 

  10. Freese, R., ‘Free modular lattices’, Trans. Amer. Math. Soc. 261 (1980), 81–91.

    Article  MathSciNet  MATH  Google Scholar 

  11. Freese, R., McKenzie, R., ‘Residually small varieties with modular congruence lattices’, Trans. Amer. Math. Soc. 264 (1981), 419–430.

    Article  MathSciNet  MATH  Google Scholar 

  12. Freese, R., McKenzie, R., Commutator Theory for Congruence Modular Varieties, London Math. Soc. Lecture Note Ser. 125 (Cambridge University Press, Cambridge, 1987).

    MATH  Google Scholar 

  13. Golubov, E. A., Sapir, M. V., ‘Varieties of finitely approximable semigroups’, Soviet Math. Dokl. 20 (1979), 828–832.

    MathSciNet  MATH  Google Scholar 

  14. Grätzer, G., General Lattice Theory (Academic Press, New York, 1978).

    Book  MATH  Google Scholar 

  15. Grätzer, G., Universal Algebra, Second Edition (Springer-Verlag, New York, 1979).

    MATH  Google Scholar 

  16. Gross, H., Herrmann, C., Moresi, R., ‘The classification of subspaces in Hermitean vector spaces’, J. Algebra 105 (1987), 516–541.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  18. Herrmann, C., ‘On the word problem for the modular lattice with four free generators’, Math. Ann. 256 (1983), 513–527.

    Article  MathSciNet  MATH  Google Scholar 

  19. Hobby, D., McKenzie, R., The Structure of Finite Algebras, Contemporary Math. 76 (Amer. Math. Soc., Providence, 1988).

    MATH  Google Scholar 

  20. Kurosh, A. G., Lectures on General Algebra (Chelsea Publ. Co., New York, 1965).

    MATH  Google Scholar 

  21. Lampe, W., ‘A property of lattices of equational theories’, Algebra Universalis 23 (1986), 61–69.

    Article  MathSciNet  MATH  Google Scholar 

  22. Mal’cev, A. I., Algebraic Systems (Springer-Verlag, New York, 1973).

    Book  Google Scholar 

  23. McKenzie, R., ‘On finite groupoids and K-prime algebras’, Trans. Amer. Math. Soc. 133 (1968), 115–129.

    MathSciNet  MATH  Google Scholar 

  24. McKenzie, R., ‘Cardinal multiplication of structures with a reflexive relation’, Fund. Math. 70 (1971), 59–101.

    MathSciNet  MATH  Google Scholar 

  25. McKenzie, R., ‘Residually small varieties of semigroups’, Algebra Universalis 13 (1981), 171–201.

    Article  MathSciNet  MATH  Google Scholar 

  26. McKenzie, R., ‘Narrowness implies uniformity’, Algebra Universalis 15 (1982a), 67–85.

    Article  MathSciNet  MATH  Google Scholar 

  27. McKenzie, R., ‘Residually small varieties of K-algebras’, Algebra Universalis 14 (1982b), 181–196.

    Article  MathSciNet  MATH  Google Scholar 

  28. McKenzie, R., ‘A note on residually small varieties of semigroups’, Algebra Universalis 17 (1983), 143–149.

    Article  MathSciNet  MATH  Google Scholar 

  29. McKenzie, R. N., McNulty, G. F., Taylor, W. F., Algebras, Lattices, Varieties, vol. I (Wadsworth and Brooks/Cole, Monterey, California, 1987).

    MATH  Google Scholar 

  30. McKenzie, R., Valeriote, M., The Structure of Decidable Locally Finite Varieties, Progress in Math. 79 (Birkhauser, Boston, 1989).

    Book  MATH  Google Scholar 

  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).

    Chapter  Google Scholar 

  32. Ol’shanskii, A. Yu., ‘Varieties of finitely approximable groups’, Math. USSR—Izv. 3 (1969), 867–877 (1971).

    MATH  Google Scholar 

  33. Ol’shanskii, A. Yu., ‘Conditional identities in finite groups’, Siber. Math. J. 15 (1974), 1000–1003 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  35. Pigozzi, D., ‘Finite basis theorems for relatively congruence-distributive quasivarieties’, Proc. Amer. Math. Soc. (to appear).

    Google Scholar 

  36. Power, S. C., ‘Infinite tensor products of upper triangular matrix algebras’, Math. Scand. (1989) (to appear).

    Google Scholar 

  37. Power, S. C., ‘Classifications of tensor products of operator algebras’ (preprint).

    Google Scholar 

  38. Sapir, M. V., ‘Problems of Burnside type and the finite basis property in varieties of semigroups’, Math. USSR—Izv. 30 (1988a), 295–314.

    MathSciNet  Google Scholar 

  39. Sapir, M. V., ‘Inherently nonfinitely based finite semigroups’, Math. USSR—Sb. 61 (1988b), 155–166.

    MathSciNet  MATH  Google Scholar 

  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. Smith, J. D. H., Mal’cev Varieties, Lecture Notes in Math. 554 (Springer-Verlag, Berlin, 1976).

    Book  MATH  Google Scholar 

  42. Taylor, W., ‘Residually small varieties’, Algebra Universalis 2 (1972), 33–53.

    Article  MathSciNet  MATH  Google Scholar 

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L. G. Kovács

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© 1990 Springer-Verlag

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McKenzie, R. (1990). Some interactions between group theory and the general theory of algebras. In: Kovács, L.G. (eds) Groups—Canberra 1989. Lecture Notes in Mathematics, vol 1456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100729

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  • DOI: https://doi.org/10.1007/BFb0100729

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  • Print ISBN: 978-3-540-53475-4

  • Online ISBN: 978-3-540-46900-1

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