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1979•Proceedings of the Edinburgh Mathematical SocietyRequires access

Centralisers in Wreath Products

J. D. P. Meldrum

Open publisher page 5 citations

Abstract

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

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What this paper is about

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

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Available abstract

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

Key concepts: Wreath product, Mathematics, Product (mathematics), Pointwise, Combinatorics, Element (criminal law), Group (periodic table), Pure mathematics

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