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A theorem on infinite groups

Published online by Cambridge University Press:  24 October 2008

Gilbert Baumslag
Gilbert Baumslag
Affiliation:
The UniversityManchester 13
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Extract

It is well known ((1), pp. 120–1) that if G is a finite p–group then the factor group G/G′ is cyclic if and only if G is itself cyclic. A trivial consequence of this fact is that, in such a case, the factor group G′/G″ is the unit group. (As usual, G(r) denotes the rth derived group of the group G.)

We prove the following theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 3 , July 1957 , pp. 545 - 548
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

(1)Burnside, W.Theory of groups of finite order, 2nd ed. (New York, 1954).Google Scholar
(2)Zassenhaus, H.The theory of groups (New York, 1949).Google Scholar