group(deprecated)/isnormal - Maple Help

group(deprecated)

 isnormal
 determine whether a subgroup is normal

 Calling Sequence isnormal(subgrl) isnormal(pg, sg)

Parameters

 subgrl - subgrel pg, sg - two permgroups of the same degree

Description

 • Important: The group package has been deprecated. Use the superseding command GroupTheory[IsNormal] instead.
 • 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.
 • With one argument, this function tests whether subgrl is a normal subgroup.  The function returns true or false.
 • The command with(group,isnormal) allows the use of the abbreviated form of this command.

Examples

Important: The group package has been deprecated. Use the superseding command GroupTheory[IsNormal] instead.

 > $\mathrm{with}\left(\mathrm{group}\right):$
 > $\mathrm{pg}≔\mathrm{permgroup}\left(8,\left\{\left[\left[1,2\right]\right],\left[\left[1,2,3,4,5,6,7,8\right]\right]\right\}\right):$
 > $\mathrm{sg1}≔\mathrm{permgroup}\left(8,\left\{\left[\left[1,2,3,4\right]\right],\left[\left[1,2\right]\right],\left[\left[5,6,7,8\right]\right],\left[\left[5,6\right]\right]\right\}\right):$
 > $\mathrm{isnormal}\left(\mathrm{pg},\mathrm{sg1}\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{sg2}≔\mathrm{permgroup}\left(8,\left\{\left[\left[1,2,3\right]\right],\left[\left[2,3,4,5,6,7,8\right]\right]\right\}\right):$
 > $\mathrm{isnormal}\left(\mathrm{pg},\mathrm{sg2}\right)$
 ${\mathrm{true}}$ (2)
 > $g≔\mathrm{grelgroup}\left(\left\{a,b\right\},\left\{\left[a,a,a,a,a\right],\left[b,b,b\right],\left[a,b,\frac{1}{a},\frac{1}{b}\right]\right\}\right):$
 > $\mathrm{isnormal}\left(\mathrm{subgrel}\left(\left\{x=\left[a\right]\right\},g\right)\right)$
 ${\mathrm{true}}$ (3)