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Commutator subgroups of finite p-groups

To Bernhard Hermann Neumann on his 60th birthday

Published online by Cambridge University Press:  09 April 2009

James Wiegold
James Wiegold
Affiliation:
Australian National University, University College, Cardiff
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Within five minutes of the start of my first meeting with Bernhard Neumann as his research student, late in 1954, he suggested the following problem to me. Let G be a group in which the cardinals of the classes of conjugate elements are boundedly finite with maximum η, say. Then the commutator subgroup G′ is finite [6], Is the order |G′| of G′ bounded in terms of n? I distinctly recall these words of Neumann: “That should provide us with a start, I think”. He was right: more than just a start, the problem has been a continuing stimulus to a study of questions in fields as far apart as permutation group theory ([7], [11], [12], [14], and some unpublished work of Peter M. Neumann) and multiplicator theory ([13], [2]), as well as attracting interest in its own right.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 3-4 , November 1969 , pp. 480 - 484
Copyright
Copyright © Australian Mathematical Society 1969

References

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