Book Review: Generators and relations for discrete groups
نویسندگان
چکیده
منابع مشابه
Generators and Relations for Certain Special Linear Groups
Several years ago I calculated presentations for several of the groups SL(2, R) where R is the ring of integers of a quadratic imaginary number field K = Q((—in)). The method used was extremely tedious and was never published. Recently, while checking these calculations, I discovered a much simpler approach to the problem which I will outline here. The interest in these calculations is consider...
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it is shown that there are exactly seventy-eight 3-generator 2-groups of order $2^{11}$ with trivial schur multiplier. we then give 3-generator, 3-relation presentations for forty-eight of them proving that these groups have deficiency zero.
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We give an elementary proof that there are two topological generators for the full group of every aperiodic hyperfinite probability measure preserving Borel equivalence relation. Our proof explicitly constructs topological generators for the orbit equivalence relation of the irrational rotation of the circle, and then appeals to Dye’s theorem and a Baire category argument to conclude the genera...
متن کاملPresentations of Topological Full Groups by Generators and Relations
We describe generators and defining relations for the commutator subgroup of topological full groups of minimal subshifts. We show that the world problem in a topological full group is solvable if and only if the language of the underlying subshift is recursive.
متن کاملGenerators and Relations for K
Tate’s algorithm for computing K2OF for rings of integers in a number field has been adapted for the computer and gives explicit generators for the group and sharp bounds on their order—the latter, together with some structural results on the p-primary part of K2OF due to Tate and Keune, gives a proof of its structure for many number fields of small discriminants, confirming earlier conjectural...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1958
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1958-10178-0