论文信息 - On the laws of a metabelian variety

On the laws of a metabelian variety

Many varieties of groups are known to have a finite basis for their laws (for the definition and general properties of varieties, see [6]-[8]). Among such varieties are any variety consisting of nilpotent groups of bounded class [4] and any variety generated by a finite group [9]. It is not known whether all varieties have a finite basis for their laws. In this paper we prove the following theorem.

D. E Cohen | D. Cohen

[1] H. Neumann. On varieties of groups and their associated near-rings , 1956 .

[2] P. Hall,et al. Finiteness Conditions for Soluble Groups , 1954 .

[3] Two notes on nilpotent groups , 1952 .

[4] M. Powell,et al. Identical relations in finite groups , 1964 .

[5] Wilhelm Magnus,et al. On a Theorem for Marshall Hall , 1939 .

[6] Sheila Oates,et al. Identical Relations in Groups , 1963 .

[7] B. H. Neumann. Identical relations in groups. I , 1937 .

[8] H. Neumann. Varieties of Groups , 1967 .

[9] R. Fox,et al. Free differential calculus. I : Derivation in the free group ring , 1953 .

[10] Graham Higman,et al. Ordering by Divisibility in Abstract Algebras , 1952 .