Graham Higman’s lectures on januarials

This is an account of a series of lectures of Graham Higman on januarials, namely coset graphs for actions of triangle groups which become 2-face maps when embedded in orientable surfaces. Spilt Milk We that have done and thought, That have thought and done, Must ramble, and thin out Like milk spilt on a stone. The Nineteenth Century and After Though the great song return no more There’s keen delight in what we have: The rattle of pebbles on the shore Under the receding wave. from The Winding Stair and Other Poems, W.B.Yeats, 1933 1 Preamble Graham Higman gave the lectures on which this article is based, in Oxford in 2001. They are likely to have been the final lectures he gave; he died in April 2008, at the age of 91. He introduced them with the quotes from W.B. Yeats reproduced above, and [email protected], http://www.math.auckland.ac.nz/∼conder/ [email protected], http://www.math.cornell.edu/∼riley/