#4105: multiplication of permutations in distinct subgroups sometimes doesn't 
work
--------------------------+-------------------------------------------------
 Reporter:  was           |       Owner:  joyner    
     Type:  defect        |      Status:  new       
 Priority:  minor         |   Milestone:  sage-3.1.3
Component:  group_theory  |    Keywords:            
--------------------------+-------------------------------------------------
 I think the following session (reported by Beezer) says it all:

 {{{
 tetra=AlternatingGroup(4)
 stab1=PermutationGroup_subgroup(tetra, ["(1,2,3)"])
 stab4=PermutationGroup_subgroup(tetra, ["(2,3,4)"])
 for g in stab1:
  for h in stab4:
    print g*h
 ///

 Traceback (most recent call last):       print g*h
   File "/home/wstein/sage/local/lib/python2.5/site-
 packages/SQLAlchemy-0.4.6-py2.5.egg/", line 3, in <module>

   File "element.pyx", line 1090, in
 sage.structure.element.MonoidElement.__mul__
 (sage/structure/element.c:7938)
   File "coerce.pyx", line 651, in
 sage.structure.coerce.CoercionModel_cache_maps.bin_op
 (sage/structure/coerce.c:6154)
   File "permgroup_element.pyx", line 463, in
 sage.groups.perm_gps.permgroup_element.PermutationGroupElement._r_action
 (sage/groups/perm_gps/permgroup_element.c:3598)
   File "permgroup_element.pyx", line 254, in
 sage.groups.perm_gps.permgroup_element.PermutationGroupElement.__init__
 (sage/groups/perm_gps/permgroup_element.c:2097)
   File "/home/wstein/sage/local/lib/python2.5/site-
 packages/sage/groups/perm_gps/permgroup_named.py", line 134, in __init__
     raise ValueError, "n (=%s) must be >= 1"%n
 ValueError: n (=0) must be >= 1
 }}}

 {{{
 tetra=AlternatingGroup(4)
 stab1=PermutationGroup_subgroup(tetra, ["(1,2,3)"])
 stab4=PermutationGroup_subgroup(tetra, ["(2,3,4)"])
 for g in stab1:
  for h in stab4:
    print tetra(g)*tetra(h)
 ///

 ()
 (2,3,4)
 (2,4,3)
 (1,2,3)
 (1,3)(2,4)
 (1,4,3)
 (1,3,2)
 (1,4,2)
 (1,2)(3,4)
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4105>
SAGE <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of 
Reinventing the Wheel
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