Hello everyone, I was thinking of Implementing *Permutation group triple product property* as suggested by *S.Y. Lee* here (https://github.com/sympy/sympy/issues/18525 ). You can see more about it using these two links: 1.)https://en.wikipedia.org/wiki/Triple_product_property 2.)https://arxiv.org/pdf/1104.5097.pdf
*Permutation group triple product property: *(Reference Wikipedia) Let {\displaystyle G}[image: G] be a non-trivial group. Three nonempty subsets {\displaystyle S,T,U\subset G}[image: {\displaystyle S,T,U\subset G}] are said to have the *triple product property* in {\displaystyle G}[image: G] if for all elements {\displaystyle s,s'\in S}[image: {\displaystyle s,s'\in S}], {\displaystyle t,t'\in T}[image: {\displaystyle t,t'\in T}], {\displaystyle u,u'\in U}[image: {\displaystyle u,u'\in U}] it is the case that {\displaystyle s's^{-1}t't^{-1}u'u^{-1}=1\Rightarrow s'=s,t'=t,u'=u}[image: {\displaystyle s's^{-1}t't^{-1}u'u^{-1}=1\Rightarrow s'=s,t'=t,u'=u}] where {\displaystyle 1}[image: 1] is the identity of {\displaystyle G}[image: G]. So there is one algorithm mentioned in here (2.) https://arxiv.org/pdf/1104.5097.pdf Which is given below. Here *S, T, U *are *subgroups.* So I am expriencing some problem in implementation of this algorithm. - As we can see intersection is used here and till now sympy does not contain any function for *intersection of two groups*. - We can also see that here we are interested in finding whether the intersection of two subgroups is *trivial* or not so maybe se can avoid calculating intersection for of two groups. - I was also thinking of using property "T*wo Normal Subgroups Intersecting Trivially Commute Each Other*" ( https://yutsumura.com/two-normal-subgroups-intersecting-trivially-commute-each-other/) but this will work only for *Normal groups*. Can we have discussion that what should be the best approach here? def test(S, T, U): if( T ∩ U = 1 ) then if( S ∩ T · U = 1 ) then return true; fi; fi; return false; -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/eb793771-4064-47d3-8c44-6cc88da6dd5f%40googlegroups.com.