Dear GAP Forum,
On Dec 5, 2010, at 12/5/10 6:57, Johannes Wachs wrote: > Is there a way to call up the multiplicative group of order n? You could create Z/nZ in GAP as Units(Integers mod 75); (or whatever modulus you like). > > In particular I have written a program to output some set of positive > integers. I want to test if they are a subgroup of the multiplicative group > mod n. It would be great if I could use Subgroup(G, L); > > Alternatively, I think I could solve my problem by checking to see if my set > is closed under multiplication mod n. Is there a way to implement IsGroup > for some set mod n with multiplication? If you create a group in GAP, the convention is that GAP will take the multiplicative closure of this generating set. Thus -- unless you wanted to compare elements -- `Subgroup' will not help for testing whether a set is a group. Similarly `IsGroup' is declared in GAP as a category, i.e. a property that an object will have from creation, but that is not testable. (I.e. if you define a semigroup, even if it turns out to be a group, it will never fulfill `IsGroup'.) In the case of your problem, I fear that fundamentally you will have to test closure (though the fact that it is a subset of an abelian group with known base will allow for some shortcuts). Best, Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hul...@math.colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
