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Centralisers in Wreath Products

Published online by Cambridge University Press:  20 January 2009

J. D. P. Meldrum
J. D. P. Meldrum
Affiliation:
University of Edinburgh
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In this paper, the centraliser of an arbitrary element of a wreath product is determined. One application of this is to find the breadth of a wreath product (Theorems 21 and 22), a problem which was raised in discussion with Dr. I. D. Macdonald. Another application is to groups generated by elements generating their own centralisers (Theorem 20).

Let A and B be two groups. Define

AB = {f : B → A; f(b) = e for all but a finite number of elements of B} to be a group by defining the product pointwise

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 2 , June 1979 , pp. 161 - 168
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1) MacDonald, I. D., The breadth of finite p-groups I, Proc. A. Royal Soc. Edinburgh. 78 (1977–1978), 31–39.CrossRefGoogle Scholar
(2) Shield, D., Power and commutator structure of groups, Bull. Austral. Math. Soc. 15 (1976), 315–317.CrossRefGoogle Scholar
(3) Wells, C., Some applications of the wreath product construction, American Math. Monthly 83 (1976), 317–338.CrossRefGoogle Scholar