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A problem of Paul Erdös on groups

Published online by Cambridge University Press:  09 April 2009

B. H. Neumann
B. H. Neumann
Affiliation:
The Australian National University, and Commonwealth Scientific and Industrial Research Organization, Division of Mathematics and Statistics, Canberra, Australia
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Let G be a group, and associate with G a graph 1 γ = Γ (G) as follows: the vertices of Γ are the elements of G, and two vertices g, h of Γ are joined by an undirected edge if, and only if, g and h do not commute as elements of G, that is [g, h] ≠ 1 [where [g, h] is the commutator g−1h−1gh, and 1 is the unit element of the groups that occur as well as the integer, according to context].We are interested in complete subgraphs of Γ, or equivalently in sets of elements of G no two of which commute.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 4 , June 1976 , pp. 467 - 472
Copyright
Copyright © Australian Mathematical Society 1976

References

Neumann, B. H. (1955), ‘Groups with finite classes of conjugate subgroups’, Math. Z. 63, 76–96.CrossRefGoogle Scholar
Derek, J. S. Robinson (1972), Finiteness conditions and generalized soluble groups, Part 1 (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 62. Springer-Verlag, Berlin, Heidelberg, New York 1972).Google Scholar