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Journal of the London Mathematical Society 1987 s2-35(2):287-295; doi:10.1112/jlms/s2-35.2.287
© 1987 by London Mathematical Society
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© Oxford University Press

The Number of Pairwise Non-Commuting Elements and the Index of the Centre in a Finite Group

L. Pyber

Mathematical Institute of the Hungarian Academy of Sciences Budapest, POB 127, 1364 Hungary

If the group G contains at most n pairwise non-commuting elements, then |G:Z(G)| ≤ cn for some constant c. This answers a question of B. H. Neumann and also solves a problem of P. Erdös.


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