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group[isnormal] - determine whether a subgroup is normal
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Calling Sequence
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isnormal(subgrl)
isnormal(pg, sg)
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Parameters
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subgrl
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subgrel
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pg, sg
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two permgroups of the same degree
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Description
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With two arguments, this function determines whether sg is a normal subgroup of the permutation group generated by the union of sg and pg. If it is, then true is returned; otherwise false is returned.
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With one argument, this function tests whether subgrl is a normal subgroup. The function returns true or false.
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The command with(group,isnormal) allows the use of the abbreviated form of this command.
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Examples
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![pg := permgroup(8, {[[1, 2]], [[1, 2, 3, 4, 5, 6, 7, 8]]})](/support/helpjp/helpview.aspx?si=8722/file04189/math85.png)
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![sg1 := permgroup(8, {[[1, 2]], [[5, 6]], [[1, 2, 3, 4]], [[5, 6, 7, 8]]})](/support/helpjp/helpview.aspx?si=8722/file04189/math89.png)
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![sg2 := permgroup(8, {[[1, 2, 3]], [[2, 3, 4, 5, 6, 7, 8]]})](/support/helpjp/helpview.aspx?si=8722/file04189/math100.png)
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![g := grelgroup({a, b}, {[b, b, b], [a, b, 1/a, 1/b], [a, a, a, a, a]})](/support/helpjp/helpview.aspx?si=8722/file04189/math111.png)
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![isnormal(subgrel({x = [a]}, g))](/support/helpjp/helpview.aspx?si=8722/file04189/math115.png)
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| (3) |
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