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Conformality and p-isomorphism in finite nilpotent groups

Published online by Cambridge University Press:  09 April 2009

C. D. H. Cooper
C. D. H. Cooper
Affiliation:
Queen Mary College, London
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This paper discusses the relationship between two equivalence relations on the class of finite nilpotent groups. Two finite groups are conformal if they have the same number of elements of all orders. (Notation: G ≈ H.) This relation is discussed in [4] pp 107–109 where it is shown that conformality does not necessarily imply isomorphism, even if one of the groups is abelian. However, if both groups are abelian the position is much simpler. Finite conformal abelian groups are isomorphic.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 2 , May 1967 , pp. 165 - 171
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Hall, Marshall, The theory of groups (Macmillan, 1959).Google Scholar
[2]Hardy, G. H. and Wright, E. M., The theory of numbers (Oxford, 1959).Google Scholar
[3]Jones, B. W., The theory of numbers (Constable, 1955).Google Scholar
[4]Miller, G. A., Blichfeldt, H. F. and Dickson, L. E., Theory and applications of finite groups (Wiley, 1916).Google Scholar