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
group theory.