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A finite basis theorem for product varieties of groups

Published online by Cambridge University Press:  17 April 2009

M.S. Brooks ,
L.G. Kovács  and
M.F. Newman
M.S. Brooks
Affiliation:
Australian National University, Canberra, ACT.
L.G. Kovács
Affiliation:
Australian National University, Canberra, ACT.
M.F. Newman
Affiliation:
Australian National University, Canberra, ACT.
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Abstract

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It is shown that, if U is a subvariety of the join of a nilpotent variety and a metabelian variety and if V is a variety with a finite basis for its laws, then UV also has a finite basis for its laws. The special cases U nilpotent and U metabelian have been established by Higman (1959) and Ivanjuta (1969) respectively. The proof here, which is independent of Ivanjuta's, depends on a rather general sufficient condition for a product variety to have a finite basis for its laws.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 1 , February 1970 , pp. 39 - 44
Copyright
Copyright © Australian Mathematical Society 1970

References

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