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In this expository note we provide a proof of Artins theorem which states that the commutator subgroup of a free group on two generators is not finitely generated. The proof employs the infinite grid as in two other proofs in the literature mentioned in the note but takes a somewhat different approach which seems to be of didactic value.
In real Hilbert spaces, this paper generalizes the orthogonal groups $mathrm{O}(n)$ in two ways. One way is by finite multiplications of a family of operators from reflections which results in a group denoted as $Theta(kappa)$, the other is by consid
We incorporate covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. We work with all covers that arise from extensions of quasisplit reductive groups by $mathbf{K}_2$ -- the class studied b
We extend the notions of quasi-monomial groups and almost monomial groups, in the framework of supercharacter theories, and we study their connection with Artins conjecture regarding the holomorphy of Artin $L$-functions.
In 1992, Osamu Kakimizu defined a complex that has become known as the Kakimizu complex of a knot. Vertices correspond to isotopy classes of minimal genus Seifert surfaces of the knot. Higher dimensional simplices correspond to collections of such cl
General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes convincing evidence? I will argue that, given the types of evidence that are currently accepted as convinc