Please note that the functions below are implemented only for PcpGroups. They are (currently) very inefficient, so use with caution.
‣ Intersection( C1, C2, ... ) | ( function ) |
‣ Intersection( list ) | ( function ) |
‣ Intersection2( C1, C2 ) | ( operation ) |
Calculates the intersection of the (right) cosets C1, C2, ... Alternatively, list may be a list of (right) cosets. This intersection is either a new coset, or an empty list.
gap> G := ExamplesOfSomePcpGroups( 5 );; gap> H := Subgroup( G, [ G.1*G.2^-1*G.3^-1*G.4^-1, G.2^-1*G.3*G.4^-2 ] );; gap> K := Subgroup( G, [ G.1*G.3^-2*G.4^2, G.1*G.4^4 ] );; gap> x := G.1*G.3^-1;; gap> y := G.1*G.2^-1*G.3^-2*G.4^-1;; gap> Hx := RightCoset( H, x );; gap> Ky := RightCoset( K, y );; gap> Intersection( Hx, Ky ); RightCoset(<group with 2 generators>,<object>)
5.2-1 \in‣ \in( g, D ) | ( operation ) |
Given an element g of a PcpGroup and a double coset D of that same group, this function tests whether g is an element of D.
gap> HxK := DoubleCoset( H, x, K );; gap> G.1 in HxK; false gap> G.2 in HxK; true
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