Alex Malcolm

Width questions for finite simple groups

Width questions concern covering a given group G with elements from a normal subset, using products of minimal length. For example, if it is known that a fixed conjugacy class generates a group, it is then natural to ask how quickly this generation happens. Can we write every group element as a product of two or perhaps three elements from this class?
Such problems often require the application of interesting results from character theory and in particular, ordinary characters of minimal degree. In this talk we will consider recent work concerning finite simple groups and elements of prime order.