ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 01 Sep 2022 11:15:56 +0200How to construct direct product of cyclic groupshttps://ask.sagemath.org/question/63875/how-to-construct-direct-product-of-cyclic-groups/If I use
D = direct_product_permgroups([G1,G2])
where
G1 = CyclicPermutationGroup(3)
G2 = CyclicPermutationGroup(4)
then I get D presented as a subgroup of SymmetricGroup(7). Is there a way to obtain the product of G1 and G2 as a subgroup of SymmetricGroup(12)?
More generally, is there a way to obtain direct product of CyclicPermutationGroup(n1) and CyclicPermutationGroup(n2) as a subgroup of SymmetricGroup(n1 n2) rather than SymmetricGroup(n1+n2)?abhijitgThu, 01 Sep 2022 11:15:56 +0200https://ask.sagemath.org/question/63875/Direct product for finitely presented groupshttps://ask.sagemath.org/question/10367/direct-product-for-finitely-presented-groups/I am currently trying to implement a direct product function for finitely presented groups by wrapping GAP's DirectProduct method. I have placed a constructor <code>direct_product_groups</code>, which appears in the global namespace, in the top level groups.pyx file, which accepts a list of groups as input. The function then checks the representations of the groups listed, and calls the appropriate constructor
such as <code>direct_product_permgroups</code> or <code>direct_product_fpgroups</code>,
which I am currently implementing as a private constructor.
My goal for <code>direct_product_groups</code> is that it will eventually completely mimic GAP's DirectProduct in that it takes a list of groups in any representation, and outputs their direct product in an appropriate representation. But for now, it behaves simply by punting its input to other, more specific constructors.
I was wondering if this approach is prefered, if this functionality is already implemented somewhere, or if anyone has any suggestions/thoughts/critiques at all. I'm new to Sage and want to get a feel for the response to this enhancement before it is posted to trac.
-dshurbertdshurbertSat, 20 Jul 2013 18:12:07 +0200https://ask.sagemath.org/question/10367/