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On coverings of a finite group by abelian subgroups

Published online by Cambridge University Press:  24 October 2008

David R. Mason
David R. Mason
Affiliation:
Haberdashers' Aske's School, Elstree, Hertfordshire
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Extract

In (2), Erdös and Straus pose the following two conjectures.

If G is a finite group of order n and X is a subset of G consisting of pairwise non-commuting elements, then |X| ≤ n/2 + 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 2 , March 1978 , pp. 205 - 209
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Baumann, B. Endliche Gruppen mit einer 2-zentralen Involution, deren Zentralisator 2-abgeschlossen ist. (To appear.)Google Scholar
(2)Erdös, P. and Straus, E. G.How abelian is a finite group? Linear and Multilinear Algebra 3 (1976), 307–312.CrossRefGoogle Scholar
(3)Gorenstein, D.Finite groups (New York, Harper and Row, 1968).Google Scholar
(4)Glauberman, G.Central elements in core-free groups. J. Algebra 4 (1966), 403–420.CrossRefGoogle Scholar
(5)Mason, D. R.On finite simple groups G in which every element of ℒ(G) is of Bender type. J. Algebra 40 (1976), 125–202.CrossRefGoogle Scholar