Abstract
The reader is referred to Hanna Neumann [12], [13] for notation, terminology and basic facts relating to varieties of groups. Recall that a variety of universal algebras is a class of universal algebras closed under the operations of forming subalgebras, cartesian products and quotient algebras. Equivalently a variety is the class of universal algebras satisfying a given set of identical relations (Birkoff [1]; see also Neumann [11] or Cohn [9] for varieties of universal algebras).
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References
Garrett Birkhoff, “On the structure of abstract algebras”, Proc. Cambridge Philos. Soc. 31 (1935), 433–454. FdM61,1026.
Warren Brisley, “On varieties of metabelian p-groups, and their laws”, J. Austral. Math. Soc. 7 (1967), 64–80. MR34#7646.
Warren Brisley, “Varieties of metabelian p-groups of class p, p + 1 ”, J. Austral. Math. Soc. 12 (1971), 53–62. MR43#4890.
M.S. Brooks, “On lattices of varieties of metabelian groups”, J. Austral. Math. Soc. 12 (1971), 161–166. MR45#3526.
M.S. Brooks, “On varieties of metabelian groups of prime-power exponent”, J. Austral. Math. Soc. 14 (1972), 129–154.
R.A. Bryce, “Metabelian groups and varieties”, Philos. Trans. Roy. Soc. London Ser. A 266 (1970), 281–355. MR42#349.
R.A. Bryce and John Cossey, “Some product varieties of groups”, Bull. Austral. Math. Soc. 3 (1970), 231–264. MR42#4618.
D.E. Cohen, “On the laws of a metabelian variety”, J. Algebra 5 (1967), 267–273. MR34#5929.
P.M. Cohn, Universal algebra, (Harper’s series in modern mathematics. Harper and Row, New York, Evanston, London, 1965 ). MR31#224.
L.G. Kovács and M.F. Newman, “On non-Cross varieties of groups”, J. Austral. Math. Soc. 12 (1971), 129–144. MR45#1966.
B.H. Neumann, Special Topics in Algebra: Universal Algebra, (Courant Institute of Mathematical Sciences, New York University, 1962 ).
Manna Neumann, “Varieties of groups”, Proc. Internat. Conf. Theory of Groups, (Canberra, 1965), pp. 251–259, ( Gordon and Breach, New York, London, Paris, 1967 ). MR35#6733.
Hanna Neumann, Varieties of groups, (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37. Springer-Verlag, Berlin, Heidelberg, New York, 1967 ). MR35#6734.
Elizabeth A. Ormerod, “A non-distributive metabelian variety lattice”, these Proc.
А.Л. Шмелькин [A.L. Šmel’kin], “Сплетения и многообразия групп” [Wreath products and varieties of groups], Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), 149–170. MR33#1352.
Paul M. Weichsel, “On metabelian p-groups”, J. Austral. Math. Soc. 7 (1967), 55–63. MR34#7645.
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© 1974 Springer-Verlag Berlin Heidelberg
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Bryce, R.A. (1974). Metabelian Varieties of Groups. In: Newman, M.F. (eds) Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21571-5_12
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