# Ticket #10920: trac_10920-conjugates-permutation-groups.patch

File trac_10920-conjugates-permutation-groups.patch, 3.6 KB (added by rbeezer, 10 years ago)
• ## sage/groups/perm_gps/permgroup.py

# HG changeset patch
# User Rob Beezer <beezer@ups.edu>
# Date 1299903500 28800
# Node ID 1c93228470c548dce9903f841338cf6cce449597
# Parent  8438b7c20d79c02a2ece3e1c3f7224a772ff8f07
10920: conjugates of permutation groups

diff -r 8438b7c20d79 -r 1c93228470c5 sage/groups/perm_gps/permgroup.py
 a C = self._gap_().Center() return PermutationGroup(gap_group=C) def conjugate(self, g): r""" Returns the group formed by conjugating self with g. INPUT: - g - a permutation group element, or an object that converts to a permutation group element, such as a list of integers or a string of cycles. OUTPUT: If self is the group denoted by H, then this method computes the group .. math:: g^{-1}Hg = \{g^{-1}hg\vert h\in H\} which is the group H conjugated by g. There are no restrictions on self and g belonging to a common permutation group, and correspondingly, there is no relationship (such as a common parent) between self and the output group. EXAMPLES:: sage: G = DihedralGroup(6) sage: a = PermutationGroupElement("(1,2,3,4)") sage: G.conjugate(a) Permutation Group with generators [(1,5,6,2,3,4), (1,4)(2,6)(3,5)] The element performing the conjugation can be specified in several ways.  :: sage: G = DihedralGroup(6) sage: strng = "(1,2,3,4)" sage: G.conjugate(strng) Permutation Group with generators [(1,5,6,2,3,4), (1,4)(2,6)(3,5)] sage: G = DihedralGroup(6) sage: lst = [2,3,4,1] sage: G.conjugate(lst) Permutation Group with generators [(1,5,6,2,3,4), (1,4)(2,6)(3,5)] sage: G = DihedralGroup(6) sage: cycles = [(1,2,3,4)] sage: G.conjugate(cycles) Permutation Group with generators [(1,5,6,2,3,4), (1,4)(2,6)(3,5)] Conjugation is a group automorphism, so conjugate groups will be isomorphic. :: sage: G = DiCyclicGroup(6) sage: G.degree() 11 sage: cycle = [i+1 for i in range(1,11)] + [1] sage: C = G.conjugate(cycle) sage: G.is_isomorphic(C) True The conjugating element may be from a symmetric group with larger degree than the group being conjugated.  :: sage: G = AlternatingGroup(5) sage: G.degree() 5 sage: g = "(1,3)(5,6,7)" sage: H = G.conjugate(g); H Permutation Group with generators [(1,4,6,3,2), (1,4,6)] sage: H.degree() 6 The conjugating element is checked. :: sage: G = SymmetricGroup(3) sage: G.conjugate("junk") Traceback (most recent call last): ... TypeError: junk does not convert to a permutation group element """ try: g = PermutationGroupElement(g) except: raise TypeError("{0} does not convert to a permutation group element".format(g)) return PermutationGroup(gap_group=gap.ConjugateGroup(self, g)) def direct_product(self,other,maps=True): """ Wraps GAP's DirectProduct, Embedding, and Projection.