Peter Neumann, The Queen's College, Oxford
Galois' Second Memoir
Èvariste Galois died aged twenty, shot in a duel.
In spite of the
shortness and turbulence of his life he left manuscripts which
fundamentally changed the theory of equations and laid the foundations
for Modern Algebra.
His Second Mémoire, written in 1830, is a difficult and much
misunderstood manuscript. Its first part deals with primitive equations
that are soluble by radicals, its second with the structure of
two-dimensional linear groups over the integers modulo a prime number.
In this lecture I shall concentrate only on the first part and focus on
three questions---what did Galois mean by `primitive', is his main
theorem correct, and how did the notion of primitivity develop in group
theory from 1830 to 1870? The lecture will be a mixture of some history
of the theory of equations with some fairly modern permutation