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Unlike many other terms in mathematics which have a universally understood meaning (for instance, "group"), the term classical group seems to have a fuzzier definition. Apparently it originates with …

The list of finite simple groups of Lie type has been understood for half a century, modulo some differences in notation (and identifications between some of the very small groups coming from differen …

In their treatise Groupes et algebres de Lie, Bourbaki (no doubt heavily influenced by Tits) devoted Chapter IV (1968) to the general theory of what they dubbed "Coxeter systems" $(W,S)$ along with "T …

Steinberg's lecture at the 1966 ICM in Moscow here surveyed his work on regular elements of semisimple algebraic groups, while also formulating a number of then-open questions as "problems" (with posi …

It may help to have some explicit bibliographic references, though some items are by now out of print and may be difficult to locate even through libraries. First, the 1966 paper by Gorenstein is lo …

Given a finite (irreducible real) group $G$ generated by reflections acting on euclidean $n$-space, it was shown by Chevalley in the 1950s that the algebra of invariants of $G$ in the associated polyn …

The answer to the question is yes, though I don't have all the old literature at my fingertips. This kind of question for various classes of linear groups has a long history in the study of homomorphi …

The narrow question here concerns the history of one development in group theory, but the broader context involves the sometimes loose use of the term "conjecture". This goes back to older work of …

To fill in the comments, there are basically two serious issues involved. 1) You want to know that every subgroup of finite index in $\mathrm{SL}(3,\mathbb{Z})$ contains some congruence kernel: the k …

Recently I've been going over some of Serre's reformulation of Brauer theory with a student, following the influential treatment in Part III of Serre's lectures (revised 1971 French edition) later pub …

It's not easy to explain the motivation without being one of the authors, but in fact Lusztig has provided some helpful perspective on the writing of his joint paper with Deligne (1976) and his earlie …

In the abstract Bourbaki set-up, the affine Weyl group is defined to be a semidirect product of an irreducible Weyl group with its coroot lattice. This is naturally a Coxeter group, characterized in t …

To reinforce Geoff's answer, I'd emphasize that the "fairly standard exercise" mentioned in the question is only standard when you consider characteristic 0 irreducible representations as is usually d …

Given a finite group $G= H \ltimes N$ (with no particular constraints on $H, N$), it's probably been known for a long time how to describe efficiently the possible subgroups of $G$. A graduate stude …

In the literature and in some posts here, there has been variation in the undefined use of the term "block" for a category of modules over a ring, or more abstractly an abelian category (all of which …