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Commutators and abelian groups

Published online by Cambridge University Press:  09 April 2009

D. M. Rodney
D. M. Rodney
Affiliation:
147 Station Road, Hendon, London, England.
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Abstract

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If G is a group, then K(G) is the set of commutators of elements of G. C is the class of groups such that G′ = K(G) is the minimal cardinality of any generating set of dG. We prove: Theorem A. Let G be a nilpotent group of class two such that G' is finite and d(G′) < 4.Then G < G.

Theorm B. Let G be a finite group such that G′ is elementary abelian of order p3. Then G ∈ C.

Theorem C. Let G be a finite group with an elementary abelian Sylow p-subgroup S, of order p2, such that S ⊆ K(G). Then S ⊆K(G).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1977 , pp. 79 - 91
Copyright
Copyright © Australian Mathematical Society 1977

References

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