@@ -4108,18 +4108,34 @@ def isomorphism_type_info_simple_group(self):
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def minimal_normal_subgroups (self ):
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"""
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- Return all minimal normal subgroups of the group.
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+ Return a list containing all minimal normal subgroups of the group.
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EXAMPLES::
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- sage: G = SymmetricGroup(4)
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- sage: G.minimal_normal_subgroups()
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- [ Group([ (1,4)(2,3), (1,3)(2,4) ]) ]
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+ sage: G = PermutationGroup([(1,2,3),(4,5)])
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+ sage: G.minimal_normal_subgroups()
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+ [Subgroup generated by [(4,5)] of (Permutation Group with generators [(4,5), (1,2,3)]),
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+ Subgroup generated by [(1,2,3)] of (Permutation Group with generators [(4,5), (1,2,3)])]
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"""
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gap_subgroups = self .gap ().MinimalNormalSubgroups ()
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sage_subgroups = [self .subgroup (gap_group = gap_subgroup ) for gap_subgroup in gap_subgroups ]
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return sage_subgroups
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+ def maximal_normal_subgroups (self ):
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+ """
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+ Return a list containing those proper normal subgroups of the group G that are maximal among the proper normal subgroups.
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+ Gives error if G/G' is infinite, yielding infinitely many maximal normal subgroups.
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+
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+ EXAMPLES::
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+
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+ sage: G = SymmetricGroup(4)
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+ sage: G.maximal_normal_subgroups()
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+ [Subgroup generated by [(2,3,4), (1,2,3)] of (Symmetric group of order 4! as a permutation group)]
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+ """
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+ gap_subgroups = self .gap ().MaximalNormalSubgroups ()
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+ sage_subgroups = [self .subgroup (gap_group = gap_subgroup ) for gap_subgroup in gap_subgroups ]
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+ return sage_subgroups
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+
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###################### Boolean tests #####################
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def is_abelian (self ):
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