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Ensuring commutativity of finite groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

B. H. Neumann
B. H. Neumann
Affiliation:
School of Mathematical Sciences, Australian National University, ACT 0200, Australia
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Abstract

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Comments are made on the following question. Let m, n be positive integers and g a finite group. Suppose that for all choices of a subset of cardinality m and of a subset of cardinality n in g some member of the first commutes with some member of the second. Under what conditions on m, n is the group abelian?

MSC classification

Secondary: 20D99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 2 , October 2001 , pp. 233 - 234
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Bell, H. E. and Klein, A. A., ‘Combinatorial commutativity and finiteness for rings II’, Preprint.Google Scholar
[2]Pakianathan, J. and Shankar, K., ‘Nilpotent number’, Amer. Math. Monthly 107 (2000), 631–634.CrossRefGoogle Scholar