![]() ![]() Is not consistent in the literature, we use the following:ģa Diagonal, Socle consists of two normal subgroups.Ĥa Product action with the first factor primitive of type 3a.Ĥb Product action with the first factor primitive of type 3b.Ĥc Product action with the first factor primitive of type 2.Īs it can contain letters, the type is returned as a string. Returns the type of G of a primitive permutation group G, according Such a group is a group isomorphic to a natural alternating group.įor a permutation group grp this function returns the symmetric group ![]() Is true if the group group is isomorphic to a natural symmetric group. There are no methods yet for IsSymmetricGroup and IsAlternatingGroup! Is isomorphic to a symmetric or alternating group. ![]() The following functions can be used to check whether a given group Groups, very efficient methods for computing membership, conjugacy classes, If so then the group is called a natural symmetric or alternating group,Ī group is a natural symmetric group if it is a permutation group actingĪ group is a natural alternating group if it is a permutation groupĪcting as alternating group on its moved points.įor groups that are known to be natural symmetric or natural alternating Or alternating group on the set of its moved points GAP can also detect whether a given permutation group is a symmetric The commands SymmetricGroup and AlternatingGroup (see Basic Groups)Ĭonstruct symmetric and alternating permutation groups. Gap> small:= SmallerDegreePermutationRepresentation( image ) Gap> image:= Image( iso ) NrMovedPoints( image ) Not guaranteed to be the same for different calls of Permutation representation (or even the degree of the representation) is The methods used might involve the use of random elements and the The degree of which may be smaller than the original degree. In this case, the actions on the cosets of these subgroups give rise toĪn intransitive permutation representation Of small index for which the cores intersect trivially Using GAP interactively, one might be able to choose subgroups Or of smallest degree among the transitive permutation representations Note that the result is not guaranteed to be a faithful permutation ![]() In the worst case this is the identity mapping on G. The result is a group homomorphism onto a permutation group, Permutation representation of smaller degree. SmallerDegreePermutationRepresentation tries to find a faithful Let G be a permutation group that acts transitively
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