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Note on a theorem of R. Baer

Published online by Cambridge University Press:  24 October 2008

G. Higman
G. Higman
Affiliation:
Department of MathematicsManchester University
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Extract

It is trivial that a group all of whose elements except the identity have order two is Abelian; and F. Levi and B. L. van der Waerden(1) have shown that a group all of whose elements except the identity have order three has class less than or equal to three. On the other hand, R. Baer(3) has shown that if the fact that all the elements of a group have orders dividing n implies a limitation on the class of the group, then n is a prime. The object of the present note is to extend this result by showing that if M is a fixed integer there are at most a finite number of prime powers n other than primes, such that the fact that all the elements of a group have orders dividing n implies a limitation on the class of its Mth derived group.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 3 , July 1949 , pp. 321 - 327
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

(1)Levi, F. and van der Waerden, B. L.Abh. Math. Sem. Hamburg, 9 (1933), 154.CrossRefGoogle Scholar
(2)Hall, P.Proc. London Math. Soc. (2), 36 (1933), 29.Google Scholar
(3)Baer, R.Bull. American Math. Soc. 50 (1943), 143.CrossRefGoogle Scholar