continued from April 29
Wikipedia on the Klein group (denoted V, for Vierergruppe):
In this representation, V is a normal subgroup of the alternating group A4 (and also the symmetric group S4) on 4 letters. In fact, it is the kernel of a surjective map from S4 to S3. According to Galois theory, the existence of the Klein four-group (and in particular, this representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals.
For radicals of another sort, see A Logocentric Meditation, A Mass for Lucero, and Steven Erlanger in The New York Times— "France Still Divided Over Lessons of 1968 Unrest."
The Klein Group as Kernel
of a Map from S4 to S3:
For those who prefer Galois's
politics to his mathematics,
there is
MAY 68: STREET POSTERS
FROM THE PARIS REBELLION
at London's Southbank Centre
(May 1 – June 1, 2008).