A theorem on infinite groups
Published online by Cambridge University Press: 24 October 2008
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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