Sentence examples for a finite presentation for from inspiring English sources

Suppose that P = [ X ; r ] is a finite presentation for a monoid ℳ.

Depending on these numbers, we define χ ( G ) = min { χ ( P ) : P  is a finite presentation for  G }.

For Claim (iv), consider a finite presentation of (G), namely a free group (F) on a finite set (S) and a normal subgroup (M) of (F) generated as normal subgroup by a finite subset (R) of (F), such that (G = F/M).

Then (langle S mid R cup R^{prime } rangle ) is a finite presentation of (G/N).

The method of the bar-complex apparently settles the problem of calculating the cohomology groups of a K(G, 1) space, and also to calculate the cohomology groups ( H^n (X, {mathbb {Q}})) for a rational K(G, 1) space X, except that one must have a good knowledge of the group G, for instance a finite presentation does not always suffice.

For example, for every hyperbolic group the word problem is solvable, and every hyperbolic group has a finite presentation.

Now, assume that (Gamma ) has a finite presentation begin{aligned} Gamma = langle x_1, ldots, x_n | R_1 x), ldots, R_m (x) rangle.

For a finitely presented semigroup, a Dehn function does not depend on the choice of finite presentation (up to equivalence), and the equivalence class of that function is called the Dehn function of the semigroup.

Appendix A: On soluble groups, metabelian groups, and finite presentations.

"We're drawing down a finite reserve for reasons that are not warranted.

And with the technology still in its infancy, defining a finite framework for its security is a challenging task.