In this paper we give an explicit and constructive description of the pairs (p. A) of elements in the symmetric group S, which can be realized as the image of the meridian-longitude pair of some knot K in the 3-sphere S3 under a representation xi (S’ K) -t S,,. The result is applied to give an otherwise nonobvious restriction on the numbers of branch curves of a branched covering , of S’, answe...

This paper and its sequel [17] deal with a range of questions about the subgroup structure of infinite symmetric groups. Our concern is with such questions as the following. How can an infinite symmetric group be expressed as the union of a chain of proper subgroups? What are the subgroups that supplement the normal subgroups of an infinite symmetric group? What are the maximal proper subgroups...

The convolution of indicators of two conjugacy classes on the symmetric group Sq is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys–Murphy element involves many conjugacy classes with complicated coefficients. In this article we consider a combinatorial setup which allows us to manipulate such products easily and...