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Identical relations and decision procedures for groups

Published online by Cambridge University Press:  09 April 2009

Hermann Heineken  and
Peter M. Neumann
Hermann Heineken
Affiliation:
Mathematisches Seminar der Universität 6 Frankfurt am Main
Peter M. Neumann
Affiliation:
The Queen's College Oxford
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Although varieties of groups can in theory be determined as well by the identical relations which the groups all satisfy as by some structural property inherited by subgroups, factor groups and cartesian products which the groups have in common, it seems in practice just as hard to answer questions about properties of a group from knowledge of identical relations as it is from, say, a presentation. Many of the important questions connected with Burnside's problems exemplify this difficulty: we still do not know if there is a bound on the derived length of finite groups of exponent 4, nor whether there is a bound on the nilpotency class of finite groups of exponent p (p ≧ 5, a fixed prime).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 1 , February 1967 , pp. 39 - 47
Copyright
Copyright © Australian Mathematical Society 1967

References

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