P.S. At the moment the AMS book mentioned earlier is on sale online: Exposition by Emil Artin: A Selection - Michael Rosen, Brown University, Editor - AMS | LMS, 2006, 346 pp., Softcover, ISBN-10: 0-8218-4172-6, ISBN-13: 978-0-8218-4172-3, List: US$59, All AMS Members: US$47, Sale Price: US$38, HMATH/30

Older books are not without value, including Cartan-Eilenberg, but it's hard to recommend them currently when books by Weibel, Rotman, and Gelfand-Manin are available. Probably the 1971 Springer text A Course in Homological Algebra by Hilton-Stammbach is a better choice among the early books than Northcott. But for later books the choice depends a lot on your preferred style and whether you want to study derived categories, Freyd-Mitchell, etc. Also whether your motivation for the subject comes from topology, algebra, representation theory, ...

@Mark: Your referee was more honest than most. Having been involved in refereeing hundreds of papers over many decades, I know how demanding the job can be. Editors usually make it clear that the referee is not responsible for the correctness of a proof but should make a reasonable effort to evaluate it.

This is a highly readable and fascinating view of Weil's early life from his own later perspective, translated (quite well it seems) from the French original and published by Birkhauser. In the absence of a full biography of Weil this is worthwhile for those who have been influenced by his mathematical legacy. Where else can one learn that Trotsky once slept in Weil's bed in Paris while Weil himself was away?

Nasar approached Nash's life and work from her background as an economics reporter, so some mathematical details get out of focus. She did a good job of talking with relevant people in Princeton and elsewhere about the period involved, though Nash himself didn't cooperate and therefore much of his life story is filtered through his ex-wife/wife. There are minor errors of detail in the book, such as misidentifications of people, but Nasar did a reasonable job with the materials she had. Unlike the movie version, she included even Nash's arrest and loss of security clearance.

To reinforce what Ben says, the standard definition of "reductive" Lie algebra in characteristic 0 just tells you that it is the direct sum of a semisimple and an abelian Lie algebra. The semisimple ones are characterized by having a nondegenerate Killing form (and resulting rich structure), while the abelian ones are just boring vector spaces. Even for algebraic groups, "reductive" has strong representation-theoretic implications only in characteristic 0; but the structure is interesting in any characteristic and over various ground fields.

Ore's book is certainly narrow but still useful for many purposes. (Ore himself was quite a nice man and allowed me to pass a German reading exam in math without asking too much of me. He was also a real mathematician unlike some people who write at the popular level.

Bell's old "biographical" book Men of Mathematics [sic] is sometimes entertaining but also often fictionalized, so I'd approach it with extra caution. I do feel that it's difficult to interest anyone in math history who isn't already somewhat drawn to math. Why bother learning about that stuff? It's like teaching 17th century French history to people with no interest in the reign of Louis XIV (though I confess to being partial to the music from that era).

Thanks, this looks very helpful and will be passed along. I suspected some literature must exist on questions like this.

Thanks for the further references, which overlap Noah's somewhat but include other interesting directions.

@Kevin: The wording may be more precise now? @Jack: You are quite right that very small groups with few classes don't provide surprises. I think the question came from a need to know about a class of groups having possibly large orders. The asker of the question should be able to enlighten me, but limiting the question is helpful. It seems too open-ended.